This book takes readers through an exploration of fundamental discussions that redefined mathematics and its philosophical significance in the centuries foregoing modernity. From William of Auvergne's paradoxes of infinity to Christoph Clavius' interpretation of Euclidean principles, it examines the evolving understanding of central issues among which continuity, the existence of mathematical objects such as numbers, and the way humans can make true statements regarding such things. Each chapter sheds light on how premodern scholars bridged mathematics and philosophy, forging concepts and approaches that continued to influence early modern thought. A compelling read for historians, philosophers, and anyone intrigued by the origins and enduring legacy of mathematical ideas as both tools for inquiry and objects of reflection.
Contributors are Joel Biard, Stephen Clucas, Clelia V. Crialesi, Vincenzo De Risi, Daniel Di Liscia, Andre Goddu, Kamil Majcherek, Paolo Mancosu, Aurelien Robert, Sabine Rommevaux, Sylvain Roudaut, and Cecilia Trifogli.
Reihe
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Für höhere Schule und Studium
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 22 mm
Gewicht
ISBN-13
978-90-04-72952-0 (9789004729520)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Clelia V. Crialesi is a Marie Sklodowska-Curie Fellow at SPHERE-CNRS (Paris, France). Her research focuses on premodern mathematical thought, with publications ranging from Boethian number theory to Euclidean geometry in the late medieval continuum debate and epistemology of 14th-century algebraic practices. She is the author of the monograph Mathematics and Philosophy at the Turn of the First Millennium. Abbo of Fleury on Calculus (Routledge, 2025).
List of Figures and Tables
Notes on Contributors
Introduction
Part 1 13th Century
1 William of Auvergne on Paradoxes of Infinity
?Paolo Mancosu
2 John Duns Scotus and Walter Chatton on Geometry and the Composition of a Continuum
?Cecilia Trifogli
3 A Science of mathematicalia in Radulphus Brito's Questiones mathematice
?Sabine Rommevaux
Part 2 14th Century
4 Can an Accident Inhere in More Than One Subject? A Problem for Medieval Realism about Numbers
?Kamil Majchereck
5 Marco Trevisano on the Ontology of Numbers: A Pythagorean and Platonic Philosophy of Mathematics
?Aurelien Robert
6 Conceiving Mathematical Terms and Propositions in the 14th Century
?Clelia V. Crialesi
Part 3 15th Century
7 The "Latitudes of Forms" as a New Middle Science
?Daniel A. Di Liscia
8 The Use of Richard Swineshead's Calculationes in 15th-Century Natural Philosophy
?Sylvain Roudaut
9 From Blasius of Parma to Alexander Achillini: A New Conception of Relations Between Mathematics and Physics
?Joel Biard
Part 4 16th Century
10 The Derivability Theory of Axioms: Logic and Mistranslations in the Middle Ages and the Renaissance
?Vincenzo De Risi
11 Beyond the Praeface: John Dee's Contributions to Henry Billingsley's Euclid and French Humanist Commentaries on Book X of Euclid's Elements
?Stephen Clucas
12 The Renaissance of Greek Mathematics and Early Modern Empiricism
?Andre Goddu
Bibliography
Index
