G W Leibniz Interrelations Between Mathematics And Philosophy

Author : Norma B. Goethe,Philip Beeley,David Rabouin
Publisher : Springer
Page : 215 pages
File Size : 53,9 Mb
Release : 2015-04-20
Category : Science
ISBN : 9789401796644

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G.W. Leibniz, Interrelations between Mathematics and Philosophy by Norma B. Goethe,Philip Beeley,David Rabouin Pdf

Up to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.

Author : Michael Otte,Marco Panza
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 42,9 Mb
Release : 1997
Category : History
ISBN : 0792345703

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Analysis and Synthesis in Mathematics by Michael Otte,Marco Panza Pdf

The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 52,8 Mb
Release : 2021
Category : Mathematics
ISBN : 9780198809647

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The History of Continua by Stewart Shapiro,Geoffrey Hellman Pdf

Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Author : M. B. W. Tent
Publisher : CRC Press
Page : 262 pages
File Size : 45,6 Mb
Release : 2011-10-17
Category : Mathematics
ISBN : 9781439892220

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Gottfried Wilhelm Leibniz by M. B. W. Tent Pdf

Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus focuses on the life and accomplishments of one of the seventeenth century’s most influential mathematicians and philosophers. The book, which draws on Leibniz’s written works and translations, and reconstructs dialogues Leibniz may have had based on the historical record of his life experiences, portrays Leibniz as both a phenomenal genius and a real person. Suitable for middle school age readers, the book traces Leibniz’s life from his early years as a young boy and student to his later work as a court historian. It discusses the intellectual and social climate in which he fought for his ideas, including his rather contentious relationship with Newton (both claimed to have invented calculus). The text describes how Leibniz developed the first mechanical calculator that could handle addition, subtraction, multiplication, and division. It also examines his passionate advocacy of rational arguments in all controversial matters, including the law, expressed in his famous exclamation calculemus: let us calculate to see who is right. Leibniz made groundbreaking contributions to mathematics and philosophy that have shaped our modern views of these fields.

Author : Vincenzo De Risi
Publisher : Springer Nature
Page : 304 pages
File Size : 52,7 Mb
Release : 2020-01-01
Category : Science
ISBN : 9783030255725

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Leibniz and the Structure of Sciences by Vincenzo De Risi Pdf

The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 47,5 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031408465

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Handbook of the History and Philosophy of Mathematical Practice by Bharath Sriraman Pdf

Author : Lloyd Strickland,Erik Vynckier,Julia Weckend
Publisher : Springer
Page : 354 pages
File Size : 50,8 Mb
Release : 2016-11-15
Category : Mathematics
ISBN : 9783319388304

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Tercentenary Essays on the Philosophy and Science of Leibniz by Lloyd Strickland,Erik Vynckier,Julia Weckend Pdf

This book presents new research into key areas of the work of German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716). Reflecting various aspects of Leibniz’s thought, this book offers a collection of original research arranged into four separate themes: Science, Metaphysics, Epistemology, and Religion and Theology. With in-depth articles by experts such as Maria Rosa Antognazza, Nicholas Jolley, Agustín Echavarría, Richard Arthur and Paul Lodge, this book is an invaluable resource not only for readers just beginning to discover Leibniz, but also for scholars long familiar with his philosophy and eager to gain new perspectives on his work.

Author : Vincenzo De Risi
Publisher : Birkhäuser
Page : 195 pages
File Size : 45,7 Mb
Release : 2016-01-28
Category : Mathematics
ISBN : 9783319198637

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Leibniz on the Parallel Postulate and the Foundations of Geometry by Vincenzo De Risi Pdf

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.

Author : Maria Rosa Antognazza
Publisher : Oxford University Press
Page : 928 pages
File Size : 48,5 Mb
Release : 2018-10-01
Category : Philosophy
ISBN : 9780190913632

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The Oxford Handbook of Leibniz by Maria Rosa Antognazza Pdf

The extraordinary breadth and depth of Leibniz's intellectual vision commands ever increasing attention. As more texts gradually emerge from seemingly bottomless archives, new facets of his contribution to an astonishing variety of fields come to light. This volume provides a uniquely comprehensive, systematic, and up-to-date appraisal of Leibniz's thought thematically organized around its diverse but interrelated aspects. Discussion of his philosophical system naturally takes place of pride. A cluster of original essays revisit his logic, metaphysics, epistemology, philosophy of nature, moral and political philosophy, and philosophy of religion. The scope of the volume, however, goes beyond that of a philosophical collection to embrace all the main features of Leibniz's thought and activity. Contributions are offered on Leibniz as a mathematician (including not only his calculus but also determinant theory, symmetric functions, the dyadic, the analysis situs, probability and statistics); on Leibniz as a scientist (physics and also optics, cosmology, geology, physiology, medicine, and chemistry); on his technical innovations (the calculating machine and the technology of mining, as well as other discoveries); on his work as an 'intelligencer' and cultural networker, as jurist, historian, editor of sources and librarian; on his views on Europe's political future, religious toleration, and ecclesiastical reunification; on his proposals for political, administrative, economic, and social reform. In so doing, the volume serves as a unique cross-disciplinary point of contact for the many domains to which Leibniz contributed. By assembling leading specialists on all these topics, it offers the most rounded picture of Leibniz's endeavors currently available.

Author : Helier J. Robinson
Publisher : Lulu.com
Page : 255 pages
File Size : 43,9 Mb
Release : 2007-09
Category : Mathematics
ISBN : 9780978363512

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Relation Philosophy of Mathematics, Science, and Mind by Helier J. Robinson Pdf

Author : Emily Rolfe Grosholz
Publisher : Springer
Page : 274 pages
File Size : 44,8 Mb
Release : 2018-11-13
Category : Mathematics
ISBN : 9783319982311

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Great Circles by Emily Rolfe Grosholz Pdf

This volume explores the interaction of poetry and mathematics by looking at analogies that link them. The form that distinguishes poetry from prose has mathematical structure (lifting language above the flow of time), as do the thoughtful ways in which poets bring the infinite into relation with the finite. The history of mathematics exhibits a dramatic narrative inspired by a kind of troping, as metaphor opens, metonymy and synecdoche elaborate, and irony closes off or shifts the growth of mathematical knowledge. The first part of the book is autobiographical, following the author through her discovery of these analogies, revealed by music, architecture, science fiction, philosophy, and the study of mathematics and poetry. The second part focuses on geometry, the circle and square, launching us from Shakespeare to Housman, from Euclid to Leibniz. The third part explores the study of dynamics, inertial motion and transcendental functions, from Descartes to Newton, and in 20th c. poetry. The final part contemplates infinity, as it emerges in modern set theory and topology, and in contemporary poems, including narrative poems about modern cosmology.

Author : Lloyd Strickland,Harry R. Lewis
Publisher : MIT Press
Page : 243 pages
File Size : 50,9 Mb
Release : 2022-10-25
Category : Mathematics
ISBN : 9780262372121

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Leibniz on Binary by Lloyd Strickland,Harry R. Lewis Pdf

The first collection of Leibniz’s key writings on the binary system, newly translated, with many previously unpublished in any language. The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today’s digital computing. This book offers the first collection of Leibniz’s most important writings on the binary system, all newly translated by the authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz’s original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz’s mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz’s development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age.

Author : Daniel Garber,Donald Rutherford
Publisher : Oxford Studies in Early Modern
Page : 323 pages
File Size : 45,7 Mb
Release : 2019-01-29
Category : Philosophy
ISBN : 9780198829294

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Oxford Studies in Early Modern Philosophy by Daniel Garber,Donald Rutherford Pdf

Oxford Studies in Early Modern Philosophy is an annual series, presenting a selection of the best current work in the history of early modern philosophy. It focuses on the seventeenth and eighteenth centuries--the extraordinary period of intellectual flourishing that begins, very roughly, with Descartes and his contemporaries and ends with Kant. It also publishes papers on thinkers or movements outside of that framework, provided they are important in illuminating early modern thought. The articles in OSEMP will be of importance to specialists within the discipline, but the editors also intend that they should appeal to a larger audience of philosophers, intellectual historians, and others who are interested in the development of modern thought.

Author : Julia Weckend,Lloyd Strickland
Publisher : Routledge
Page : 320 pages
File Size : 44,9 Mb
Release : 2019-08-19
Category : Philosophy
ISBN : 9781351595476

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Leibniz’s Legacy and Impact by Julia Weckend,Lloyd Strickland Pdf

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz’s profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned with Leibniz’s legacy and impact in a particular area, and between them they show not just the depth of Leibniz’s talents but also the extent to which he shaped the various domains to which he contributed, and in some cases continues to shape them today. With essays written by experts such as Nicholas Jolley, Pauline Phemister, and Philip Beeley, this volume is essential reading not just for students of Leibniz but also for those who wish to understand the game-changing impact made by one of history’s true universal geniuses.

Author : Richard T. W. Arthur
Publisher : Oxford University Press
Page : 368 pages
File Size : 53,6 Mb
Release : 2018-09-26
Category : Philosophy
ISBN : 9780192542151

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Monads, Composition, and Force by Richard T. W. Arthur Pdf

Leibniz's monads have long been a source of fascination and puzzlement. If monads are merely immaterial, how can they alone constitute reality? In Monads, Composition and Force, Richard T. W. Arthur takes seriously Leibniz's claim of introducing monads to solve the problem of the composition of matter and motion. Going against a trend of idealistic interpretations of Leibniz's thought, Arthur argues that although monads are presupposed as the principles making actual each of the infinite parts of matter, bodies are not composed of them. He offers a fresh interpretation of Leibniz's theory of substance in which monads are enduring primitive forces, corporeal substances are embodied monads, and bodies are aggregates of monads, not mere appearances. In this reading the monads are constitutive unities, constituting an organic unity of function through time, and bodies are phenomenal in two senses; as ever-changing things they are Platonic phenomena and as pluralities, in being perceived together, they are also Democritean phenomena. Arthur argues for this reading by describing how Leibniz's thought is grounded in seventeenth century atomism and the metaphysics of the plurality of forms, showing how his attempt to make this foundation compatible with mechanism undergirds his insightful contributions to biological science and the dynamical foundations he provides for modern physics.