Leibniz on the Parallel Postulate and the Foundations of Geometry
Leibniz on the Parallel Postulate and the Foundations of Geometry

Author: Vincenzo De Risi

Publisher: Birkhäuser

Published: 2016-01-28

Total Pages: 199

ISBN-13: 3319198637

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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.

The Oxford Handbook of Leibniz
The Oxford Handbook of Leibniz

Author: Maria Rosa Antognazza

Publisher: Oxford University Press

Published: 2018-10-01

Total Pages: 928

ISBN-13: 0190913649

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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.

Leibniz and the Structure of Sciences
Leibniz and the Structure of Sciences

Author: Vincenzo De Risi

Publisher: Springer Nature

Published: 2020-01-01

Total Pages: 304

ISBN-13: 3030255727

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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.

Leibniz on Time, Space, and Relativity
Leibniz on Time, Space, and Relativity

Author: Richard T. W. Arthur

Publisher: Oxford University Press

Published: 2021-12-16

Total Pages: 421

ISBN-13: 019266560X

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In this book, Arthur gives fresh interpretations of Gottfried Leibniz's theories of time, space, and the relativity of motion, based on a thorough examination of Leibniz's manuscripts as well as his published papers. These are analysed in historical context, but also with an eye to their contemporary relevance. Leibniz's views on relativity have been extremely influential, first on Mach, and then on Einstein, while his novel approach to geometry in his analysis situs inspired many later developments in geometry. Arthur expounds the latter in some detail, explaining its relationship to Leibniz's metaphysics of space and the grounding of motion, and defending Leibniz's views on the relativity of motion against charges of inconsistency. The brilliance of his work on time, though, has not been so well appreciated, and Arthur attempts to remedy this through a detailed discussion of Leibniz's relational theory of time, showing how it underpins his theory of possible worlds, his complex account of contingency, and his highly original treatment of the continuity of time, providing formal treatments in an appendix. In other appendices, Arthur provides translations of previously untranslated writings by Leibniz on analysis situs and on Copernicanism, as well as an essay on Leibniz's philosophy of relations. In his introductory chapter he explains how the framework for the book is provided by the interpretation of Leibniz's metaphysics he defended in his earlier Monads, Composition, and Force (OUP 2018, winner of the 2019 annual JHP Book Prize for best book in the history of philosophy published in 2018).

The History of Continua
The History of Continua

Author: Stewart Shapiro

Publisher: Oxford University Press, USA

Published: 2021

Total Pages: 593

ISBN-13: 0198809646

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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.

Space
Space

Author: Andrew Janiak

Publisher: Oxford University Press

Published: 2020-01-23

Total Pages: 369

ISBN-13: 0199914117

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Recurrent questions about space have dogged philosophers since ancient times. Can an ordinary person draw from his or her perceptions to say what space is? Or is it rather a technical concept that is only within the grasp of experts? Can geometry characterize the world in which we live? What is God's relation to space? In Ancient Greece, Euclid set out to define space by devising a codified set of axioms and associated theorems that were then passed down for centuries, thought by many philosophers to be the only sensible way of trying to fathom space. Centuries later, when Newton transformed the 'natural philosophy' of the seventeenth century into the physics of the eighteenth century, he placed the mathematical analysis of space, time, and motion at the center of his work. When Kant began to explore modern notions of 'idealism' and 'realism,' space played a central role. But the study of space was transformed forever when, in 1915, Einstein published his general theory of relativity, explaining that the world is not Euclidean after all. This volume chronicles the development of philosophical conceptions of space from early antiquity through the medieval period to the early modern era. The chapters describe the interactions at different moments in history between philosophy and various other disciplines, especially geometry, optics, and natural science more generally. Fascinating central figures from the history of mathematics, science and philosophy are discussed, including Euclid, Plato, Aristotle, Proclus, Ibn al-Haytham, Nicole Oresme, Kepler, Descartes, Newton, Leibniz, Berkeley, and Kant. As with other books in the series, shorter essays, or Reflections, enrich the volume by characterizing perspectives on space found in various disciplines including ecology, mathematics, sculpture, neuroscience, cultural geography, art history, and the history of science.

Causation and Cognition in Early Modern Philosophy
Causation and Cognition in Early Modern Philosophy

Author: Dominik Perler

Publisher: Routledge

Published: 2019-07-23

Total Pages: 343

ISBN-13: 1351379380

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This book re-examines the roles of causation and cognition in early modern philosophy. The standard historical narrative suggests that early modern thinkers abandoned Aristotelian models of formal causation in favor of doctrines that appealed to relations of efficient causation between material objects and cognizers. This narrative has been criticized in recent scholarship from at least two directions. Scholars have emphasized that we should not think of the Aristotelian tradition in such monolithic terms, and that many early modern thinkers did not unequivocally reduce all causation to efficient causation. In line with this general approach, this book features original essays written by leading experts in early modern philosophy. It is organized around five guiding questions: What are the entities involved in causal processes leading to cognition? What type(s) or kind(s) of causality are at stake? Are early modern thinkers confined to efficient causation or do other types of causation play a role? What is God's role in causal processes leading to cognition? How do cognitive causal processes relate to other, non-cognitive causal processes? Is the causal process in the case of human cognition in any way special? How does it relate to processes involved in the case of non-human cognition? The essays explore how fifteen early modern thinkers answered these questions: Francisco Suárez, René Descartes, Louis de la Forge, Géraud de Cordemoy, Nicolas Malebranche, Thomas Hobbes, Baruch de Spinoza, Gottfried Wilhelm Leibniz, Ralph Cudworth, Margaret Cavendish, John Locke, John Sergeant, George Berkeley, David Hume, and Thomas Reid. The volume is unique in that it explores both well-known and understudied historical figures, and in that it emphasizes the intimate relationship between causation and cognition to open up new perspectives on early modern philosophy of mind and metaphysics.

Oxford's Savilian Professors of Geometry
Oxford's Savilian Professors of Geometry

Author: Robin Wilson

Publisher: Oxford University Press

Published: 2022-01-10

Total Pages: 256

ISBN-13: 0192639935

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The Savilian Professorships in Geometry and Astronomy at Oxford University were founded in 1619 by Sir Henry Savile, distinguished scholar and Warden of Merton College. The Geometry chair, in particular, is the earliest University-based mathematics professorship in England, predating the first Cambridge equivalent by about sixty years. To celebrate the 400th anniversary of the founding of the geometry chair, a meeting was held at the Bodleian Library in Oxford, and the talks presented at this meeting have formed the basis for this fully edited and lavishly illustrated book, which outlines the first 400 years of Oxford's Savilian Professors of Geometry. Starting with Henry Briggs, the co-inventor of logarithms, this volume proceeds via such figures as John Wallis, a founder member of the Royal Society, and Edmond Halley, via the 19th-century figures of Stephen Rigaud, Baden Powell, Henry Smith, and James Joseph Sylvester, to the 20th century and the present day. Oxford's Savilian Professors of Geometry: The First 400 Years assumes no mathematical background, and should therefore appeal to the interested general reader with an interest in mathematics and the sciences. It should also be of interest to anyone interested in the history of mathematics or of the development of Oxford and its namesake university. To all of these audiences it offers portraits of mathematicians at work and an accessible exposition of historical mathematics in the context of its times.

Kant on Reality, Cause, and Force
Kant on Reality, Cause, and Force

Author: Tal Glezer

Publisher: Cambridge University Press

Published: 2018-01-11

Total Pages: 244

ISBN-13: 1108359663

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Kant's category of reality is an often overlooked element of his Critique of Pure Reason. Tal Glezer shows that it nevertheless belongs at the core of Kant's mature critical philosophy: it captures an issue that motivated his critical turn, shaped his theory of causation, and established the role of his philosophy of science. Glezer's study traces the roots of Kant's category of reality to early modern debates over the intelligibility of substantial forms, fueled by the tension between the idea of non-extended substances and that of extended objects. This tension influenced Kant's pre-critical work, and eventually inspired his radical break towards transcendental idealism. Glezer explores the importance of reality for Kant's conceptions of cause and force, and sheds new light on his philosophy of physical science, including gravity. His book will interest scholars of Kant and of early modern philosophy, as well as historians of scientific ideas.

On Joachim Jungius’ Texturæ Contemplatio
On Joachim Jungius’ Texturæ Contemplatio

Author: Michael Friedman

Publisher: Springer Nature

Published: 2024-01-28

Total Pages: 416

ISBN-13: 3031408810

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The book offers an analysis of Joachim Jungius’ Texturæ Contemplatio - a hitherto-unpublished manuscript written in German and Latin that deals with weaving, knitting and other textile practices, attempting to present as well various fabrics and textile techniques in a scientifical and even mathematical framework. The book aims to provide the epistemological, technical and historic framework for Jungius’ manuscript, inspecting fabrics, weaving techniques as well as looms and other textile machines in Holy Roman Empire during the Early Modern Period. It also offers a unique investigation of the notion and metaphor of ‘texture’ during this period, and explores, within the wider context of the ‘meeting’ or ‘trading zones’ thesis, the relations between artisans and natural philosophers during the 17th century. The book is of interest to historians of philosophy and mathematics, as well as historians of technology.