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Author: Richard C. Brown
Publisher: World Scientific
ISBN: 9814390798
Category : Mathematics
Languages : en
Pages : 333
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Book Description
1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.
Author: Richard C. Brown
Publisher: World Scientific
ISBN: 9814390798
Category : Mathematics
Languages : en
Pages : 333
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Book Description
1. Evolution or revolution in mathematics -- 2. Issues in seventeenth century mathematics -- 3. Isaac Barrow: a foil to Leibniz -- 4. A young central European polymath -- 5. First steps in mathematics -- 6. The creation of calculus -- 7. Logic -- 8. The universal characteristic -- 9. The baroque cultural context -- 10. Epilogue -- 11. Some concluding remarks on mathematical change -- Appendices.
Author: Richard C. Brown
Publisher: World Scientific
ISBN: 9814390801
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This book is a detailed study of Gottfried Wilhelm Leibniz''s creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known OC calculiOCO Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz. This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz''s mathematical achievement or general issues in the field."
Author: Richard C Brown
Publisher: World Scientific
ISBN: 9814401617
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known “calculi” Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.
Author: Viktor Blasjo
Publisher: Academic Press
ISBN: 0128132981
Category : Mathematics
Languages : en
Pages : 284
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Book Description
Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. - Brings to light this underlying and often implicit complex of concerns that permeate early calculus - Evaluates the technical conception and mathematical construction of the geometrical method - Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus - Provides a beautifully written work of outstanding original scholarship
Author: James O'Hara
Publisher: BRILL
ISBN: 900468736X
Category : Science
Languages : en
Pages : 1091
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Book Description
Leibniz’s correspondence from his years spent in Paris (1672-1676) reflects his growth to mathematical maturity whereas that from the years 1676-1701 reveals his growth to maturity in science, technology and medicine in the course of which more than 2000 letters were exchanged with more than 200 correspondents. The remaining years until his death in 1716 witnessed above all the appearance of his major philosophical works. The focus of the present work is Leibniz's middle period and the core themes and core texts from his multilingual correspondence are presented in English from the following subject areas: mathematics, natural philosophy, physics (and cosmology), power technology (including mining and transport), engineering and engineering science, projects (scientific, technological and economic projects), alchemy and chemistry, geology, biology and medicine.
Author: Norma B. Goethe
Publisher: Springer
ISBN: 9401796645
Category : Science
Languages : en
Pages : 215
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Book Description
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: Jeff Lambert
Publisher: Rowman & Littlefield
ISBN: 1666925926
Category : Philosophy
Languages : en
Pages : 209
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Book Description
Monadological Intimacy: The Relational Operation of Folds in Leibniz and Deleuze analyzes and explains G.W. Leibniz’s theories of folds and relations to claim there is a common operation of inclusion inherent to both theories, an operation that produces a uniquely monadic form of intimacy. Utilizing key insights from Gilles Deleuze’s The Fold: Leibniz and the Baroque, Jeff Lambert considers the role of what is “virtual” and “ideal” for Leibniz in his theory of relations. However, Deleuze’s interpretation is not without flaws, and this book proposes an understanding of the operations of inclusion that is quite different from the view given by Deleuze in The Fold. Specifically, Lambert contends that relational inclusion has four primary “orders” that coincide with the four types of relations found across Leibniz’s oeuvre: complexion, comparison, congruence, and concurrence. Throughout each order of relations, different forms of interconnection play out through an intimate and immediate representation of the universe. Monadological Intimacy argues that the intimate and immediate representation of the universe within each monad utilizes the same operation of inclusion at work in how Leibniz describes the ideal continuum in each distinct fold of motion.
Author: Richard Halpern
Publisher: Columbia University Press
ISBN: 0231558767
Category : Philosophy
Languages : en
Pages : 492
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Book Description
Why read Leibniz today? Can we still learn from him and not just about him? This book argues that Leibniz offers a powerful, productive model for transdisciplinary thinking that can push back against the narrowness of the humanities today. Richard Halpern recasts Leibniz as a great writer as well as a great philosopher, demonstrating that his philosophical project cannot be fully understood without taking its literary elements into account. He shows Leibniz to be a prescient thinker about art and beauty whose insights into the relationship between aesthetic experience and thought remain invaluable. Leibnizing asks readers to follow the dynamic movement of Leibniz’s writing instead of attempting to grasp a static philosophical system and to pay careful attention to the rhetorical and stylistic registers of Leibniz’s work as well as its conceptual and logical dimensions. For philosophers, this book offers a novel approach to reading and interpreting Leibniz. For literary and other theorists, it showcases the relevance of Leibniz’s thought to areas from aesthetics to politics and from metaphysics to computer science. Written in a lucid and even witty style, Leibnizing provides readers with an accessible entryway into Leibniz’s sometimes forbidding but ultimately rewarding philosophical vision.
Author: Mircea Pitici
Publisher: Princeton University Press
ISBN: 0691160414
Category : Mathematics
Languages : en
Pages : 272
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Book Description
The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize–winning physicist Roger Penrose This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.
Author: Peter R. Anstey
Publisher: Taylor & Francis
ISBN: 1315452685
Category : History
Languages : en
Pages : 320
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Book Description
This collection of essays breaks new ground in bringing together scholars from a range of disciplines to focus on the nature and status of principles in early modern thought. A comprehensive introduction argues that there is a natural "fault line" between propositional and ontological principles, and establishes a clear understanding of how the term principle might be used, and of the kinds of questions that might be raised about its usage. With contributions from leading scholars—including Daniel Garber, William Newman, and Sophie Roux—this book will be of interest to scholars of early modern philosophy, the history of early modern thought, and the history and philosophy of science.
