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Author : Paul Rusnock
Publisher : BRILL
Page : 224 pages
File Size : 45,9 Mb
Release : 2022-06-08
Category : Philosophy
ISBN : 9789004458352
Author : Maria Zack,Elaine Landry
Publisher : Birkhäuser
Page : 248 pages
File Size : 50,5 Mb
Release : 2016-12-15
Category : Mathematics
ISBN : 9783319466156
This volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held in Washington, D.C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in these collected papers, which cover subjects such as New evidence that the Latin translation of Euclid’s Elements was based on the Arabic version attributed to al-Ḥajjāj Work done on the arc rampant in the seventeenth century The history of numerical methods for finding roots of nonlinear equations An original play featuring a dialogue between George Boole and Augustus De Morgan that explores the relationship between them Key issues in the digital preservation of mathematical material for future generations A look at the first twenty-five years of The American Mathematical Monthly in the context of the evolving American mathematical community The growth of Math Circles and the unique ways they are being implemented in the United States Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Author : Bharath Sriraman
Publisher : Springer Nature
Page : 3221 pages
File Size : 50,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031408465
Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press
Page : 320 pages
File Size : 54,7 Mb
Release : 2020-12-01
Category : Philosophy
ISBN : 9780192537492
Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.
Author : William Aspray,Philip Kitcher
Publisher : U of Minnesota Press
Page : 396 pages
File Size : 40,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780816615674
History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
Author : Dov M. Gabbay,John Woods
Publisher : Elsevier
Page : 781 pages
File Size : 40,8 Mb
Release : 2004-03-08
Category : Mathematics
ISBN : 9780080532875
With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.
Author : Stefan Roski,Benjamin Schnieder
Publisher : Oxford University Press
Page : 473 pages
File Size : 49,8 Mb
Release : 2022
Category : Mathematics
ISBN : 9780192847973
"Provides translations of Bolzano's most important work on grounding, including previously untranslated material"--
Author : S. Lapointe
Publisher : Springer
Page : 183 pages
File Size : 41,9 Mb
Release : 2011-01-28
Category : Philosophy
ISBN : 9780230308640
The first book in English to offer a systematic survey of Bolzano's philosophical logic and theory of knowledge, it offers a reconstruction of Bolzano's views on a series of key issues: the analysis of meaning, generality, analyticity, logical consequence, mathematical demonstration and knowledge by virtue of meaning.
Author : Michael Raven
Publisher : Routledge
Page : 549 pages
File Size : 55,9 Mb
Release : 2020-05-04
Category : Philosophy
ISBN : 9781351258838
Some of philosophy’s biggest questions, both historically and today, are in-virtue-of questions: In virtue of what is an action right or wrong? In virtue of what am I the same person my mother bore? In virtue of what is an artwork beautiful? Philosophers attempt to answer many of these types of in-virtue-of questions, but philosophers are also increasingly focusing on what an in-virtue-of question is in the first place. Many assume, at least as a working hypothesis, that in-virtue-of questions involve a distinctively metaphysical kind of determinative explanation called “ground.” This Handbook surveys the state of the art on ground as well as its connections and applications to other topics. The central issues of ground are discussed in 37 chapters, all written exclusively for this volume by a wide range of leading experts. The chapters are organized into the following sections: I. History II. Explanation and Determination III. Logic and Structure IV. Connections V. Applications Introductions at the start of each section provide an overview of the section’s contents, and a list of Related Topics at the end of each chapter points readers to other germane areas throughout the volume. The resulting volume is accessible enough for advanced students and informative enough for researchers. It is essential reading for anyone hoping to get clearer on what the biggest questions of philosophy are really asking.
Author : Maria Zack,Dirk Schlimm
Publisher : Birkhäuser
Page : 218 pages
File Size : 51,7 Mb
Release : 2017-12-18
Category : Mathematics
ISBN : 9783319645513
This volume contains fourteen papers that were presented at the 2016 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held at the University of Calgary in Alberta, Canada. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics, this meeting also honored the life and work of the logician and philosopher of mathematics Aldo Antonelli (1962-2015). The first four papers in this book are part of that remembrance and have a philosophical focus. Included in these are a discussion of Bolzano’s objections to Kant’s philosophy of mathematics and an examination of the influence of rhetorical and poetic aesthetics on the development of symbols in the 16th and 17th Centuries. The remaining papers deal with the history of mathematics and cover such subjects as Early schemes for polar ordinates in the work of L’Hôpital, based on lessons given to him by Bernoulli A method devised by Euler for determining if a number is a sum of two squares Playfair’s Axiom and what it reveals about the history of 19th-Century mathematics education The modern library classification system for mathematical subjects An exploration of various examples of sundials throughout Paris Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Author : J. Ferreiros,J. J. Gray
Publisher : OUP Oxford
Page : 456 pages
File Size : 42,8 Mb
Release : 2006-04-27
Category : Mathematics
ISBN : 9780191513794
This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.
Author : Anne Reboul
Publisher : Springer
Page : 530 pages
File Size : 55,6 Mb
Release : 2014-08-13
Category : Philosophy
ISBN : 9783319041995
This book addresses five main topics of metaphysics in its first section: formal objects and truth-makers; tropes; properties and predicates; varieties of relations; and the notion of explanation in metaphysics. The second part of this volume focuses on the history of philosophy with an emphasis on Austrian philosophy: the ideas of Bolzano, Wittgenstein, Locke and Bergson, amongst others, are explored in the papers presented here. This is the first volume in a two-volume set that originates from papers presented to Professor Kevin Mulligan, covering the subjects that he contributed to during his career including ontology, mind and value, history and philosophy of mind and philosophy of language. This volume contains thirty two chapters, written by researchers from across Europe, North America and North Africa. These papers cover topics in metaphysics ranging from Lehrer and Tolliver’s discussion of truth and tropes, to Johansson’s defence of the distinction between thick and thin relations and Persson and Sahlin’s presentation of the difficulties inherent in applying the concept of explanation in metaphysics. Papers on the history of philosophy include a look at Bolzano’s formative years and his conception of mathematics. De Libera examines Brentano’s adverbial theory of judgment and Fisette traces the history of the Philosophical Society of the University of Vienna in the late 19th and early 20th century. Marion contests the trendy pragmatist accounts that lump Wittgenstein and Heidegger together and there are analyses of Locke and Bergson’s work, amongst the many papers presented here. This volume contains three chapters in French and one in Spanish. The second volume of this set looks at ethics, values and emotions, epistemology, perception and consciousness, as well as philosophy of mind and philosophy of language.
Author : Ladislav Kvasz
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 42,6 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9783764388409
Kvasz’s book is a contribution to the history and philosophy of mat- matics, or, as one might say, the historical approach to the philosophy of mathematics. This approach is for mathematics what the history and philosophy of science is for science. Yet the historical approach to the philosophy of science appeared much earlier than the historical approach to the philosophy of mathematics. The ?rst signi?cant work in the history and philosophy of science is perhaps William Whewell’s Philosophy of the Inductive Sciences, founded upon their History. This was originally published in 1840, a second, enlarged edition appeared in 1847, and the third edition appeared as three separate works p- lished between 1858 and 1860. Ernst Mach’s The Science of Mech- ics: A Critical and Historical Account of Its Development is certainly a work of history and philosophy of science. It ?rst appeared in 1883, and had six further editions in Mach’s lifetime (1888, 1897, 1901, 1904, 1908, and 1912). Duhem’s Aim and Structure of Physical Theory appeared in 1906 and had a second enlarged edition in 1914. So we can say that history and philosophy of science was a well-established ?eld th th by the end of the 19 and the beginning of the 20 century. By contrast the ?rst signi?cant work in the history and philosophy of mathematics is Lakatos’s Proofs and Refutations, which was p- lished as a series of papers in the years 1963 and 1964.
Author : Stewart Shapiro,Geoffrey Hellman
Publisher : Oxford University Press, USA
Page : 593 pages
File Size : 46,9 Mb
Release : 2021
Category : Mathematics
ISBN : 9780198809647
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 : F. Prihonsky
Publisher : Springer
Page : 295 pages
File Size : 55,7 Mb
Release : 2014-10-28
Category : Philosophy
ISBN : 9781137312655
Finally available in English, Príhonský's New Anti-Kant is an inescapable book for anyone interested in Kant's Critical philosophy. It provides a concise and systematic recapitulation of Bolzano's insightful, trenchant criticisms of Kant, and provides a fresh window into historical developments in 19th century post-Kantian philosophy
