Leibniz On The Parallel Postulate And The Foundations Of Geometry

Author : Vincenzo De Risi
Publisher : Birkhäuser
Page : 195 pages
File Size : 53,7 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 : Vincenzo De Risi
Publisher : Springer Nature
Page : 304 pages
File Size : 41,5 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 : Maria Rosa Antognazza
Publisher : Oxford University Press
Page : 928 pages
File Size : 50,7 Mb
Release : 2018-10-01
Category : Philosophy
ISBN : 9780190913649

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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 : John William Withers
Publisher : Unknown
Page : 216 pages
File Size : 48,6 Mb
Release : 1905
Category : Mathematics
ISBN : UOM:39015039785400

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Euclid's Parallel Postulate by John William Withers Pdf

Author : Richard T. W. Arthur
Publisher : Oxford University Press
Page : 421 pages
File Size : 44,9 Mb
Release : 2021-12-16
Category : Philosophy
ISBN : 9780192665607

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Leibniz on Time, Space, and Relativity by Richard T. W. Arthur Pdf

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).

Author : William Barrett Frankland
Publisher : CUP Archive
Page : 100 pages
File Size : 42,5 Mb
Release : 1910
Category : Parallels (Geometry).
ISBN : 8210379456XXX

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Theories of Parallelism by William Barrett Frankland Pdf

Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 44,5 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 : Andrew Janiak
Publisher : Oxford University Press
Page : 288 pages
File Size : 51,7 Mb
Release : 2020-01-23
Category : Philosophy
ISBN : 9780199914111

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Space by Andrew Janiak Pdf

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.

Author : Dominik Perler,Sebastian Bender
Publisher : Routledge
Page : 343 pages
File Size : 42,9 Mb
Release : 2019-07-23
Category : Philosophy
ISBN : 9781351379380

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Causation and Cognition in Early Modern Philosophy by Dominik Perler,Sebastian Bender Pdf

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.

Author : Robin Wilson
Publisher : Oxford University Press
Page : 256 pages
File Size : 54,9 Mb
Release : 2022-01-10
Category : Mathematics
ISBN : 9780192639936

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Oxford's Savilian Professors of Geometry by Robin Wilson Pdf

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.

Author : Tal Glezer
Publisher : Cambridge University Press
Page : 243 pages
File Size : 42,7 Mb
Release : 2018-01-11
Category : Philosophy
ISBN : 9781108420693

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Kant on Reality, Cause, and Force by Tal Glezer Pdf

Original analysis of Kant's category of reality, with wide-ranging implications for understanding his critical philosophy and its development.

Author : Michael Friedman
Publisher : Springer Nature
Page : 416 pages
File Size : 55,7 Mb
Release : 2024-01-28
Category : Technology & Engineering
ISBN : 9783031408816

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On Joachim Jungius’ Texturæ Contemplatio by Michael Friedman Pdf

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.

Author : Jens Lemanski
Publisher : Springer Nature
Page : 318 pages
File Size : 44,8 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783030330903

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Language, Logic, and Mathematics in Schopenhauer by Jens Lemanski Pdf

The chapters in this timely volume aim to answer the growing interest in Arthur Schopenhauer’s logic, mathematics, and philosophy of language by comprehensively exploring his work on mathematical evidence, logic diagrams, and problems of semantics. Thus, this work addresses the lack of research on these subjects in the context of Schopenhauer’s oeuvre by exposing their links to modern research areas, such as the “proof without words” movement, analytic philosophy and diagrammatic reasoning, demonstrating its continued relevance to current discourse on logic. Beginning with Schopenhauer’s philosophy of language, the chapters examine the individual aspects of his semantics, semiotics, translation theory, language criticism, and communication theory. Additionally, Schopenhauer’s anticipation of modern contextualism is analyzed. The second section then addresses his logic, examining proof theory, metalogic, system of natural deduction, conversion theory, logical geometry, and the history of logic. Special focus is given to the role of the Euler diagrams used frequently in his lectures and their significance to broader context of his logic. In the final section, chapters discuss Schopenhauer’s philosophy of mathematics while synthesizing all topics from the previous sections, emphasizing the relationship between intuition and concept. Aimed at a variety of academics, including researchers of Schopenhauer, philosophers, historians, logicians, mathematicians, and linguists, this title serves as a unique and vital resource for those interested in expanding their knowledge of Schopenhauer’s work as it relates to modern mathematical and logical study.

Author : Michael T Stuart,Yiftach Fehige,James Robert Brown
Publisher : Routledge
Page : 709 pages
File Size : 49,7 Mb
Release : 2017-07-20
Category : Philosophy
ISBN : 9781351705516

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The Routledge Companion to Thought Experiments by Michael T Stuart,Yiftach Fehige,James Robert Brown Pdf

Thought experiments are a means of imaginative reasoning that lie at the heart of philosophy, from the pre-Socratics to the modern era, and they also play central roles in a range of fields, from physics to politics. The Routledge Companion to Thought Experiments is an invaluable guide and reference source to this multifaceted subject. Comprising over 30 chapters by a team of international contributors, the Companion covers the following important areas: · the history of thought experiments, from antiquity to the trolley problem and quantum non-locality; · thought experiments in the humanities, arts, and sciences, including ethics, physics, theology, biology, mathematics, economics, and politics; · theories about the nature of thought experiments; · new discussions concerning the impact of experimental philosophy, cross-cultural comparison studies, metaphilosophy, computer simulations, idealization, dialectics, cognitive science, the artistic nature of thought experiments, and metaphysical issues. This broad ranging Companion goes backwards through history and sideways across disciplines. It also engages with philosophical perspectives from empiricism, rationalism, naturalism, skepticism, pluralism, contextualism, and neo-Kantianism to phenomenology. This volume will be valuable for anyone studying the methods of philosophy or any discipline that employs thought experiments, as well as anyone interested in the power and limits of the mind.

Author : Angela Axworthy
Publisher : Springer Nature
Page : 306 pages
File Size : 53,6 Mb
Release : 2022-06-11
Category : Mathematics
ISBN : 9783030958176

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Motion and Genetic Definitions in the Sixteenth-Century Euclidean Tradition by Angela Axworthy Pdf

A significant number of works have set forth, over the past decades, the emphasis laid by seventeenth-century mathematicians and philosophers on motion and kinematic notions in geometry. These works demonstrated the crucial role attributed in this context to genetic definitions, which state the mode of generation of geometrical objects instead of their essential properties. While the growing importance of genetic definitions in sixteenth-century commentaries on Euclid’s Elements has been underlined, the place, uses and status of motion in this geometrical tradition has however never been thoroughly and comprehensively studied. This book therefore undertakes to fill a gap in the history of early modern geometry and philosophy of mathematics by investigating the different treatments of motion and genetic definitions by seven major sixteenth-century commentators on Euclid’s Elements, from Oronce Fine (1494–1555) to Christoph Clavius (1538–1612), including Jacques Peletier (1517–1582), John Dee (1527–1608/1609) and Henry Billingsley (d. 1606), among others. By investigating the ontological and epistemological conceptions underlying the introduction and uses of kinematic notions in their interpretation of Euclidean geometry, this study displays the richness of the conceptual framework, philosophical and mathematical, inherent to the sixteenth-century Euclidean tradition and shows how it contributed to a more generalised acceptance and promotion of kinematic approaches to geometry in the early modern period.