The history of continua philosophical and mathematical perspectives / edited by Stewart Shapiro and Geoffrey Hellman.
| Other author | Shapiro, Stewart, 1951- |
| Other author | Hellman, Geoffrey. |
| Other author | Oxford University Press. |
| Format | Electronic |
| Edition | First edition. |
| Publication Info | Oxford, United Kingdom ; New York, NY : Oxford University Press, 2021. |
| Description | viii, 577 pages : illustrations ; 25 cm |
| Supplemental Content | Full text available from Oxford Scholarship Online |
| Subjects |
| Contents | Introduction / Stewart Shapiro and Geoffrey Hellman -- 1. Divisibility or indivisibility : the notion of continuity from the Presocratics to Aristotle / Barbara Sattler -- 2. Contiguity, continuity and continuous change : Alexander of Aphrodisias on Aristotle / Orna Harari -- 3. Infinity and continuity : Thomas Bradwardine and his contemporaries / Edith Dudley Sylla -- 4. Continuous extension and indivisibles in Galileo / Samuel Levey -- 5. The indivisibles of the continuum : seventeenth- century adventures in infinitesimal mathematics / Douglas. M Jesseph -- 6. The continuum, the infinitely small, and the law of continuity in Leibniz / Samuel Levey -- 7. Continuity and intuition in 18th century analysis and in Kant / Daniel Sutherland -- 8. Bolzano on continuity / Paul Rusnock -- 9. Cantor and continuity / Akihiro Kanamori -- 10. Dedekind on continuity / Emmylou Haner and Dirk Schlimm -- 11. What is a number? : continua, magnitudes, quantities / Charles McCarty -- 12. Continuity and intuitionism / Charles McCarty -- 13. The Peircean continuum / Francisco Vargas and Matthew E. Moore -- 14. Points as higher-order constructs : Whitehead's method of extensive abstraction / Achille C. Varzi -- 15. The predicative conception of the continuum / Peter Koellner -- 16. Point-free continuum / Giangiacomo Gerla -- 17. Intuitionistic/constructive accounts of the continuum today / John L. Bell -- 18. Contemporary infinitesimalist theories of continua and their late nineteenth and early twentieth century forerunners / Philip Ehrlich. |
| Subject | "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. 0The 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."-- Taken from back of dust jacket. |
| Bibliography note | Includes bibliographical references and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2020938610 |
| ISBN | 9780198809647 hardcover |
| ISBN | 0198809646 hardcover |