Overview

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.

Full Product Details

Author:   Clelia V. Crialesi
Publisher:   Brill
Imprint:   Brill
Volume:   25
Weight:   0.001kg
ISBN:  

9789004729520

ISBN 10:   9004729526
Pages:   416
Publication Date:   24 July 2025
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Forthcoming
Availability:   Not yet available  
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Table of Contents

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

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Author Information

Clelia V. Crialesi is a Marie Skłodowska-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).

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