Pre-Modern Mathematical Thought

The Latin Discussion (13th-16th Centuries)
Erscheinungsjahr 2025
ISBN: 978-90-04-72952-0
Verlag: Brill

Buch, Englisch, Band 25, 370 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 758 g

Reihe: Investigating Medieval Philosophy

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 Joël Biard, Stephen Clucas, Clelia V. Crialesi, Vincenzo De Risi, Daniel Di Liscia, André Goddu, Kamil Majcherek, Paolo Mancosu, Aurélien Robert, Sabine Rommevaux, Sylvain Roudaut, and Cecilia Trifogli.

Autoren/Hrsg.

Weitere Mitwirkende

Crialesi, Clelia V.

Fachgebiete

• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie Mittelalterliche & Scholastische Philosophie
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Geisteswissenschaften Geschichtswissenschaft Alte Geschichte & Archäologie Vor- und Frühgeschichte, prähistorische Archäologie
• Geisteswissenschaften Geschichtswissenschaft Geschichtswissenschaft Allgemein

Inhaltsverzeichnis

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 Aurélien 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 Joël 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 André Goddu

Bibliography

Index

Über Autor(innen)

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).