Pre-modern Mathematical Thought

The Latin Discussion (13th-16th Centuries)

Buch | Hardcover

380 Seiten

2025
Brill (Verlag)
978-90-04-72952-0 (ISBN)

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The book focuses on the diverse manifestations of mathematical thought at the end of the Middle Ages and right before modernity, revealing how mathematics was understood as both a tool for inquiry and a subject of philosophical reflection in its own right.

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.

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).

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

Erscheinungsdatum	19.07.2025
Reihe/Serie	Investigating Medieval Philosophy ; 25
Verlagsort	Leiden
Sprache	englisch
Maße	155 x 235 mm
Gewicht	758 g
Themenwelt	Geschichte ► Allgemeine Geschichte ► Mittelalter
	Geschichte ► Allgemeine Geschichte ► Neuzeit (bis 1918)
	Geisteswissenschaften ► Geschichte ► Regional- / Ländergeschichte
	Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
ISBN-10	90-04-72952-6 / 9004729526
ISBN-13	978-90-04-72952-0 / 9789004729520
Zustand	Neuware