Philosophical Aspects Of Symbolic Reasoning In Early Modern Mathematics

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A Material History of Medieval and Early Modern Ciphers

Author : Katherine Ellison
Publisher : Routledge
ISBN 13 : 1351973088
Total Pages : 286 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis A Material History of Medieval and Early Modern Ciphers by : Katherine Ellison

Download or read book A Material History of Medieval and Early Modern Ciphers written by Katherine Ellison and published by Routledge. This book was released on 2017-09-14 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first cultural history of early modern cryptography, this collection brings together scholars in history, literature, music, the arts, mathematics, and computer science who study ciphering and deciphering from new materialist, media studies, cognitive studies, disability studies, and other theoretical perspectives. Essays analyze the material forms of ciphering as windows into the cultures of orality, manuscript, print, and publishing, revealing that early modern ciphering, and the complex history that preceded it in the medieval period, not only influenced political and military history but also played a central role in the emergence of the capitalist media state in the West, in religious reformation, and in the scientific revolution. Ciphered communication, whether in etched stone and bone, in musical notae, runic symbols, polyalphabetic substitution, algebraic equations, graphic typographies, or literary metaphors, took place in contested social spaces and offered a means of expression during times of political, economic, and personal upheaval. Ciphering shaped the early history of linguistics as a discipline, and it bridged theological and scientific rhetoric before and during the Reformation. Ciphering was an occult art, a mathematic language, and an aesthetic that influenced music, sculpture, painting, drama, poetry, and the early novel. This collection addresses gaps in cryptographic history, but more significantly, through cultural analyses of the rhetorical situations of ciphering and actual solved and unsolved medieval and early modern ciphers, it traces the influences of cryptographic writing and reading on literacy broadly defined as well as the cultures that generate, resist, and require that literacy. This volume offers a significant contribution to the history of the book, highlighting the broader cultural significance of textual materialities.

Selected Essays on Pre- and Early Modern Mathematical Practice

Author : Jens Høyrup
Publisher : Springer Nature
ISBN 13 : 303019258X
Total Pages : 963 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Selected Essays on Pre- and Early Modern Mathematical Practice by : Jens Høyrup

Download or read book Selected Essays on Pre- and Early Modern Mathematical Practice written by Jens Høyrup and published by Springer Nature. This book was released on 2019-09-20 with total page 963 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad selection of articles mainly published during the last two decades on a variety of topics within the history of mathematics, mostly focusing on particular aspects of mathematical practice. This book is of interest to, and provides methodological inspiration for, historians of science or mathematics and students of these disciplines.

Handbook of the History and Philosophy of Mathematical Practice

Author : Bharath Sriraman
Publisher : Springer Nature
ISBN 13 : 3031408462
Total Pages : 3221 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman

Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics

Author : Albrecht Heeffer
Publisher :
ISBN 13 : 9781848900172
Total Pages : 302 pages
Book Rating : 4.9/5 (1 download)

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Book Synopsis Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics by : Albrecht Heeffer

Download or read book Philosophical Aspects of Symbolic Reasoning in Early Modern Mathematics written by Albrecht Heeffer and published by . This book was released on 2010 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exists which enables us to express all knowledge? This book brings together a collection of papers that address all these and related questions ? which were initially posed on a conference held in Ghent (Belgium) in August 2009. Scholars working on philosophy of science, history of philosophy and history of mathematics provide an insight into the role and function of symbolic representations in the development of early modern mathematics. The papers cover the period from early abbaco arithmetic and algebra (14th century) up to Leibniz (early 18th century).

De Sphaera of Johannes de Sacrobosco in the Early Modern Period

Author : Matteo Valleriani
Publisher : Springer Nature
ISBN 13 : 3030308332
Total Pages : 406 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis De Sphaera of Johannes de Sacrobosco in the Early Modern Period by : Matteo Valleriani

Download or read book De Sphaera of Johannes de Sacrobosco in the Early Modern Period written by Matteo Valleriani and published by Springer Nature. This book was released on 2020-01-01 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book explores commentaries on an influential text of pre-Copernican astronomy in Europe. It features essays that take a close look at key intellectuals and how they engaged with the main ideas of this qualitative introduction to geocentric cosmology. Johannes de Sacrobosco compiled his Tractatus de sphaera during the thirteenth century in the frame of his teaching activities at the then recently founded University of Paris. It soon became a mandatory text all over Europe. As a result, a tradition of commentaries to the text was soon established and flourished until the second half of the 17th century. Here, readers will find an informative overview of these commentaries complete with a rich context. The essays explore the educational and social backgrounds of the writers. They also detail how their careers developed after the publication of their commentaries, the institutions and patrons they were affiliated with, what their agenda was, and whether and how they actually accomplished it. The editor of this collection considers these scientific commentaries as genuine scientific works. The contributors investigate them here not only in reference to the work on which it comments but also, and especially, as independent scientific contributions that are socially, institutionally, and intellectually contextualized around their authors.

Journal of Early Modern Studies - Volume 2, Issue 1 (Spring 2013)

Author : Jalobeanu, Dana
Publisher : Zeta Books
ISBN 13 : 9731997199
Total Pages : 194 pages
Book Rating : 4.7/5 (319 download)

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Book Synopsis Journal of Early Modern Studies - Volume 2, Issue 1 (Spring 2013) by : Jalobeanu, Dana

Download or read book Journal of Early Modern Studies - Volume 2, Issue 1 (Spring 2013) written by Jalobeanu, Dana and published by Zeta Books. This book was released on 2013-01-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Hesiod to Saussure, from Hippocrates to Jevons

Author : Jens Høyrup
Publisher : Springer Nature
ISBN 13 : 3031515102
Total Pages : 434 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis From Hesiod to Saussure, from Hippocrates to Jevons by : Jens Høyrup

Download or read book From Hesiod to Saussure, from Hippocrates to Jevons written by Jens Høyrup and published by Springer Nature. This book was released on 2024 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of a three-volume set introducing the history of scientific thought (including social and human science) and covers the Latin Middle Ages, the Renaissance period, and the 17th century. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

Research in History and Philosophy of Mathematics

Author : Maria Zack
Publisher : Springer Nature
ISBN 13 : 3031461932
Total Pages : 190 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Research in History and Philosophy of Mathematics by : Maria Zack

Download or read book Research in History and Philosophy of Mathematics written by Maria Zack and published by Springer Nature. This book was released on 2024-01-18 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include: A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schema A quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematicians The depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to her A study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth century An examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notes A global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentaries Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.

Making and Breaking Mathematical Sense

Author : Roi Wagner
Publisher : Princeton University Press
ISBN 13 : 0691171718
Total Pages : 250 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Making and Breaking Mathematical Sense by : Roi Wagner

Download or read book Making and Breaking Mathematical Sense written by Roi Wagner and published by Princeton University Press. This book was released on 2017-01-10 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.

Descartes's Method

Author : Tarek R. Dika
Publisher : Oxford University Press
ISBN 13 : 0192696947
Total Pages : 407 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Descartes's Method by : Tarek R. Dika

Download or read book Descartes's Method written by Tarek R. Dika and published by Oxford University Press. This book was released on 2023-02-27 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descartes's Method develops an ontological interpretation of Descartes's method as a dynamic and, within limits, differentiable problem-solving cognitive disposition or habitus, which can be actualized or applied to different problems in various ways, depending on the nature of the problem. Parts I-II develop the foundations of an habitual interpretation of Descartes's method, while Parts III-V demonstrate the fruits of such an interpretation in metaphysics, natural philosophy, and mathematics. The first book to draw on the recently discovered Cambridge manuscript of Descartes's Rules for the Direction of the Mind, Descartes's Method concretely demonstrates the efficacy of Descartes's method in the sciences and the underlying unity of Descartes's method from Rules for the Direction of the Mind to Principles of Philosophy (1644).

From Hesiod to Saussure, from Hippocrates to Jevons

Author : Jens Høyrup
Publisher : Springer Nature
ISBN 13 : 3031515064
Total Pages : 365 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis From Hesiod to Saussure, from Hippocrates to Jevons by : Jens Høyrup

Download or read book From Hesiod to Saussure, from Hippocrates to Jevons written by Jens Høyrup and published by Springer Nature. This book was released on 2024 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of a three-volume set introducing the history of scientific thought (including social and human science). The area covered in this volume is ancient Mesopotamia, classical Antiquity and the Islamic Middle Ages. Combining general descriptions with extensive excerpts from original sources in English translation, it concentrates on ways of thinking and actual argumentation and not just on results and mistakes; questions of validity are primarily dealt with in the perspective of the time of the writing, not on that of the 21st century. The work is of great interest to historians of science and culture, students as well as seasoned workers – but also for amateurs willing to invest the necessary serious efforts.

Seventeenth-Century Indivisibles Revisited

Author : Vincent Jullien
Publisher : Birkhäuser
ISBN 13 : 3319001310
Total Pages : 499 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Seventeenth-Century Indivisibles Revisited by : Vincent Jullien

Download or read book Seventeenth-Century Indivisibles Revisited written by Vincent Jullien and published by Birkhäuser. This book was released on 2015-05-19 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles ́ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.

British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750)

Author : Leo Corry
Publisher : Springer Nature
ISBN 13 : 3031115384
Total Pages : 79 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) by : Leo Corry

Download or read book British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) written by Leo Corry and published by Springer Nature. This book was released on 2022-09-12 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the changing conceptions about the relationship between geometry and arithmetic within the Euclidean tradition that developed in the British context of the sixteenth and seventeenth century. Its focus is on Book II of the Elements and the ways in which algebraic symbolism and methods, especially as recently introduced by François Viète and his followers, took center stage as mediators between the two realms, and thus offered new avenues to work out that relationship in idiosyncratic ways not found in earlier editions of the Euclidean text. Texts examined include Robert Recorde's Pathway to Knowledge (1551), Henry Billingsley’s first English translation of the Elements (1570), Clavis Mathematicae by William Oughtred and Artis Analyticae Praxis by Thomas Harriot (both published in 1631), Isaac Barrow’s versions of the Elements (1660), and John Wallis Treatise of Algebra (1685), and the English translations of Claude Dechales’ French Euclidean Elements (1685). This book offers a completely new perspective of the topic and analyzes mostly unexplored material. It will be of interest to historians of mathematics, mathematicians with an interest in history and historians of renaissance science in general.

A Brief History of Numbers

Author : Leo Corry
Publisher : OUP Oxford
ISBN 13 : 0191007072
Total Pages : 324 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis A Brief History of Numbers by : Leo Corry

Download or read book A Brief History of Numbers written by Leo Corry and published by OUP Oxford. This book was released on 2015-08-27 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.

The Oxford Handbook of Leibniz

Author : Maria Rosa Antognazza
Publisher : Oxford University Press
ISBN 13 : 0190913649
Total Pages : 928 pages
Book Rating : 4.1/5 (99 download)

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Book Synopsis The Oxford Handbook of Leibniz by : Maria Rosa Antognazza

Download or read book The Oxford Handbook of Leibniz written by Maria Rosa Antognazza and published by Oxford University Press. This book was released on 2018-10-01 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Arithmetica of Diophantus

Author : Jean Christianidis
Publisher : Taylor & Francis
ISBN 13 : 1351694979
Total Pages : 891 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis The Arithmetica of Diophantus by : Jean Christianidis

Download or read book The Arithmetica of Diophantus written by Jean Christianidis and published by Taylor & Francis. This book was released on 2022-11-01 with total page 891 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an English translation of all ten extant books of Diophantus of Alexandria’s Arithmetica, along with a comprehensive conceptual, historical, and mathematical commentary. Before his work became the inspiration for the emerging field of number theory in the seventeenth century, Diophantus (ca. 3rd c. CE) was known primarily as an algebraist. This volume explains how his method of solving arithmetical problems agrees both conceptually and procedurally with the premodern algebra later practiced in Arabic, Latin, and European vernaculars, and how this algebra differs radically from the modern algebra initiated by François Viète and René Descartes. It also discusses other surviving traces of ancient Greek algebra and follows the influence of the Arithmetica in medieval Islam, Byzantium, and the European Renaissance down to the 1621 publication of Claude-Gaspard Bachet’s edition. After the English translation the book provides a problem-by-problem commentary explaining the solutions in a manner compatible with Diophantus’s mode of thought. The Arithmetica of Diophantus provides an invaluable resource for historians of mathematics, science, and technology, as well as those studying ancient Greek, medieval Islamic and Byzantine, and Renaissance history. In addition, the volume is also suitable for mathematicians and mathematics educators.

Algorithmic Modernity

Author : Morgan G. Ames
Publisher : Oxford University Press
ISBN 13 : 0197502423
Total Pages : 313 pages
Book Rating : 4.1/5 (975 download)

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Book Synopsis Algorithmic Modernity by : Morgan G. Ames

Download or read book Algorithmic Modernity written by Morgan G. Ames and published by Oxford University Press. This book was released on 2023-01-24 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The rhetoric of algorithmic neutrality is more alive than ever-why? This volume explores key moments in the historical emergence of algorithmic practices and in the constitution of their credibility and authority since 1500. If algorithms are historical objects and their associated meanings and values are situated and contingent-and if we are to push back against rhetorical claims of otherwise-then the genealogical investigation this book offers is essential to understand the power of the algorithm. The fact that algorithms create the conditions for many of our encounters with social reality contrasts starkly with their relative invisibility. More than other artifacts, algorithms are easily black-boxed. Rather than contingent and modifiable, they are widely seen as obvious and unproblematic-without context and without history. As an antidote, this volume keeps a clear focus on the emergence and continuous reconstitution of algorithmic practices alongside the ascendance of modernity. Its essays highlight the trajectory of an algorithmic modernity, one characterized by attitudes and practices that are best emblematized by the modernist aesthetic and inhuman efficacy of the algorithm. The volume moves from early modern algorithmic practices, centered on heuristics for arithmetic operations, emphasizing ruptures, shifts, and variations across times and cultures. By the age of Enlightenment, the term algorithm had come to signify any process of systematic calculation that could be carried out mechanically, but its meaning and implications are still distant from those familiar to us . It's in the nineteenth and twentieth century that the meaning of algorithm is sharpened through a new discipline and by adding sets of specific conditions-such as the condition of finiteness-which acquire new and crucial significance in the age of digital computing. Throughout, the connection between algorithms and modernity is one of our central concerns. Through detailed historical reconstructions of specific moments, thinkers, and cultural phenomena over the last five hundred years, these essays lead us to the definitions of algorithm most legible today and to the pervasiveness of both algorithmic procedures and rhetoric. This volume contributes a multi-faceted exploration of the genealogies of algorithms, of algorithmic thinking, and of the distinctly modernist faith in algorithms as neutral tools that merely illuminate the natural and social world"--