Leibniz and the Invention of Mathematical Transcendence
Leibniz and the Invention of Mathematical Transcendence

Author: Michel Serfati

Publisher: Franz Steiner Verlag Wiesbaden GmbH

Published: 2018

Total Pages: 0

ISBN-13: 9783515120821

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The invention of mathematical transcendence in the seventeenth century is linked to Leibniz, who always claimed it to be his own creation. However, Descartes had created a completely new symbolic frame in which one considers plane curves, which was a real upheaval. Leibniz initially appreciated this Cartesian frame. Although, as we see in the book, during his research he was confronted with inexpressible contexts he then called 'transcendent'. The development of a concept of mathematical transcendence is at the core of this book. The description follows a pragmatic path by highlighting how and why aspects of the concept were developed and which obstacles were encountered by mathematicians. Also, there were some dead ends which are described here. Leibniz exceeded Descartes' ideas on a symbolical level (transcendent expressions), a geometrical level (transcendent curves) as well as a numerical level (transcendent numbers) those are also examined in detail.

Leibnizens Mathematische Schriften, Herausgegeben Von C.I. Gerhardt ...
Leibnizens Mathematische Schriften, Herausgegeben Von C.I. Gerhardt ...

Author: Gottfried Wilhelm Freiherr von Leibniz

Publisher: Theclassics.Us

Published: 1855

Total Pages: 438

ISBN-13:

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. 1860 edition.: ...pro ipso aequipollens (ut volunt) pondus C ut 1 celeritate ut 2, quod ascendat usque ad C seu ad altitudinem 4 pedum. Itaque solo descensu ponderis A duarum librarum ex altitudine unius pedis 2AH, substitutoque aequipollente, effecimus ascensum librae unius ad pedes quatuor, quod est duplum prioris. Ergo tantundem virium lucrati sumus, seu motum mechanicum perpetuum effecimus, quod utique absurdum est. Nec refert, an per motuum leges actu efficere possimus hanc substitutionem; nam inter aequipollentia etiam mente tuto fieri substitutio potest. Quamquam etiam varias rationes excogitaverimus, quibus actu tam propo quam velis efficeretur, ut vis tota corporis A transferretur in corpus C, antea quiescens, sed quod nunc (ipso A ad quietem redacto) sit solum in motu positum. Unde fieret, ut pro pondere bilibri celeritatis ut 1 successura esset libra una celeritatis ut 2, si haec aequipollerent; unde absurdum oriri ostendimus. Neque ista sane inania sunt, aut in logomachiis consistunt, sed in machinis et motibus comparandis maxiinum usum habent. Nam si quis vim habeat ab aqua vel animalibns vel alia causa, per quam corpus grave centum librarum in motu constanti conservetur, quo intra minuti temporis quartam partem absolvere possit circulum horizontalem diametri triginta pedum; alius vero ejus loco eodem tempore duplum pondus nonnisi dimidium circulum constanter absoivere praestet, minore impensa, idque tibi velut in lucrum imputet; deceptum te ac dimidia virium parte frustratum scito. Sed nunc fugatis erroribus, veras et saue admirandas Naturae leges paulo distinctius in Schediasmatis hujus parte secunda proponemus. XVI, SPECIMEN DYNAMICUM PRO ADMIRANDIS NATURAE LEGIBUS CIRCA CORPORUM VIRES ET MUTUAS ACTIONES DETEGENDIS ET AD SUAS CAUSAS REVOCANDIS. Pars II. Natura corporis, imo substantiae in universum non satis cognita effecerat (quod jam attigimus) ut insignes quidem philosophi nostri temporis, cum corporis notionem in sola extensione...

Transcendental Curves in the Leibnizian Calculus
Transcendental Curves in the Leibnizian Calculus

Author: Viktor Blasjo

Publisher: Academic Press

Published: 2017-04-22

Total Pages: 284

ISBN-13: 0128132981

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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

Nicholas of Cusa and the Making of the Early Modern World
Nicholas of Cusa and the Making of the Early Modern World

Author:

Publisher: BRILL

Published: 2019-01-14

Total Pages: 536

ISBN-13: 9004385681

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Nicholas of Cusa and Early Modern Reform sheds new light on Cusanus’ relationship to early modernity by focusing on the reform of church, the reform of theology, the reform of perspective, and the reform of method – which together aim to encompass the breadth and depth of Cusanus’ own reform initiatives. In particular, in examining the way in which he served as inspiration for a wide and diverse array of reform-minded philosophers, ecclesiastics, theologians, and lay scholars in the midst of their struggle for the renewal and restoration of the individual, society, and the world, our volume combines a focus on Cusanus as a paradigmatic thinker with a study of his concrete influence on early modern thought. This volume is aimed at scholars working in the field of late medieval and early modern philosophy, theology, and history of science. As the first Anglophone volume to explore the early modern reception of Nicholas of Cusa, this work will provide an important complement to a growing number of companions focusing on his life and thought.

And Yet It Is Heard
And Yet It Is Heard

Author: Tito M. Tonietti

Publisher: Springer

Published: 2014-05-16

Total Pages: 595

ISBN-13: 3034806752

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We bring into full light some excerpts on musical subjects which were until now scattered throughout the most famous scientific texts. The main scientific and musical cultures outside of Europe are also taken into consideration. The first and most important property to underline in the scientific texts examined here is the language they are written in. This means that our multicultural history of the sciences necessarily also becomes a review of the various dominant languages used in the different historical contexts. In this volume, the history of the development of the sciences is told as it happened in real contexts, not in an alienated ideal world.

Making up Numbers: A History of Invention in Mathematics
Making up Numbers: A History of Invention in Mathematics

Author: Ekkehard Kopp

Publisher: Open Book Publishers

Published: 2020-10-23

Total Pages: 282

ISBN-13: 1800640978

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Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

New Essays on Leibniz Reception
New Essays on Leibniz Reception

Author: Ralph Krömer

Publisher: Springer Science & Business Media

Published: 2012-03-13

Total Pages: 285

ISBN-13: 3034605048

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This book is a collection of essays on the reception of Leibniz’s thinking in the sciences and in the philosophy of science in the 19th and 20th centuries. Authors studied include C.F. Gauss, Georg Cantor, Kurd Lasswitz, Bertrand Russell, Ernst Cassirer, Louis Couturat, Hans Reichenbach, Hermann Weyl, Kurt Gödel and Gregory Chaitin. In addition, we consider concepts and problems central to Leibniz’s thought and that of the later authors: the continuum, space, identity, number, the infinite and the infinitely small, the projects of a universal language, a calculus of logic, a mathesis universalis etc. The book brings together two fields of research in the history of philosophy and of science (research on Leibniz, and the research concerned with some major developments in the 19th and 20th centuries); it describes how Leibniz’s thought appears in the works of these authors, in order to better understand Leibniz’s influence on contemporary science and philosophy; but it also assesses that reception critically, confronting it in particular with the current state of Leibniz research and with the various editions of his work.

Elements of the History of Mathematics
Elements of the History of Mathematics

Author: N. Bourbaki

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 299

ISBN-13: 3642616933

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Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.

Landmark Writings in Western Mathematics 1640-1940
Landmark Writings in Western Mathematics 1640-1940

Author: Ivor Grattan-Guinness

Publisher: Elsevier

Published: 2005-02-11

Total Pages: 1042

ISBN-13: 0080457444

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This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items. - First book of its kind - Covers the period 1640-1940 of massive development in mathematics - Describes many of the main writings of mathematics - Articles written by specialists in their field

Perspectives on Theory of Controversies and the Ethics of Communication
Perspectives on Theory of Controversies and the Ethics of Communication

Author: Dana Riesenfeld

Publisher: Springer Science & Business Media

Published: 2013-11-23

Total Pages: 222

ISBN-13: 9400771312

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Assembling an unprecedented range of considered responses to the noted contributions to philosophy made by Marcelo Dascal, this collection comprises the work of his many friends, colleagues and former students. Beginning with a series of articles on Dascal’s influential insights on philosophical controversy, this volume continues with explorations of Dascal’s celebrated scholarship on Liebnitz, before moving on to papers dealing with his philosophy of language, including interpretations by Dresner and Herring on the phenomenon of emoticons. Taken as a whole, they provide a compelling commentary on Dascal’s prolific and voluminous publications and include fresh perspectives on the theory of argumentation and the ethics of communication. The material collected here extends to political philosophy, such as Morris-Reich's paper exploring the ways in which German social scientists confront issues of antisemitism, the psychology of genius, and the origins of norms in society and culture. Much of the analysis is directly connected to, or influenced by, the philosophical themes, ideas and concepts developed throughout the years by Marcelo Dascal, while others have a looser connection to his work. All of them, however, attest to the remarkable and multifaceted philosophical persona of Marcelo Dascal, who is the guiding light of the rich conceptual dialogue running through this book. ​ ​