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Pre-modern Mathematical Thought
The Latin Discussion (13th-16th Centuries)
Series: - Investigating Medieval Philosophy, Volume: 25
Volume Editor:
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 Auvergneâs paradoxes of infinity to Christoph Claviusâ 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.
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 SkÅodowska-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
1 William of Auvergne on Paradoxes of Infinity
âPaolo Mancosu
2 John Duns Scotus and Walter Chatton on Geometry and the Composition of a Continuum
âCecilia Trifogli
3 A Science of mathematicalia in Radulphus Britoâs Questiones mathematice
âSabine Rommevaux
4 Can an Accident Inhere in More Than One Subject? A Problem for Medieval Realism about Numbers
âKamil Majchereck
5 Marco Trevisano on the Ontology of Numbers: A Pythagorean and Platonic Philosophy of Mathematics
âAurélien Robert
6 Conceiving Mathematical Terms and Propositions in the 14th Century
âClelia V. Crialesi
7 The âLatitudes of Formsâ as a New Middle Science
âDaniel A. Di Liscia
8 The Use of Richard Swinesheadâs Calculationes in 15th-Century Natural Philosophy
âSylvain Roudaut
9 From Blasius of Parma to Alexander Achillini: A New Conception of Relations Between Mathematics and Physics
âJoël Biard
10 The Derivability Theory of Axioms: Logic and Mistranslations in the Middle Ages and the Renaissance
âVincenzo De Risi
11 Beyond the Praeface: John Deeâs Contributions to Henry Billingsleyâs Euclid and French Humanist Commentaries on Book X of Euclidâs Elements
âStephen Clucas
12 The Renaissance of Greek Mathematics and Early Modern Empiricism
âAndré Goddu
Bibliography
Index
Notes on Contributors
Introduction
Part 1 13th Century
1 William of Auvergne on Paradoxes of Infinity
âPaolo Mancosu
2 John Duns Scotus and Walter Chatton on Geometry and the Composition of a Continuum
âCecilia Trifogli
3 A Science of mathematicalia in Radulphus Britoâs Questiones mathematice
âSabine Rommevaux
Part 2 14th Century
4 Can an Accident Inhere in More Than One Subject? A Problem for Medieval Realism about Numbers
âKamil Majchereck
5 Marco Trevisano on the Ontology of Numbers: A Pythagorean and Platonic Philosophy of Mathematics
âAurélien Robert
6 Conceiving Mathematical Terms and Propositions in the 14th Century
âClelia V. Crialesi
Part 3 15th Century
7 The âLatitudes of Formsâ as a New Middle Science
âDaniel A. Di Liscia
8 The Use of Richard Swinesheadâs Calculationes in 15th-Century Natural Philosophy
âSylvain Roudaut
9 From Blasius of Parma to Alexander Achillini: A New Conception of Relations Between Mathematics and Physics
âJoël Biard
Part 4 16th Century
10 The Derivability Theory of Axioms: Logic and Mistranslations in the Middle Ages and the Renaissance
âVincenzo De Risi
11 Beyond the Praeface: John Deeâs Contributions to Henry Billingsleyâs Euclid and French Humanist Commentaries on Book X of Euclidâs Elements
âStephen Clucas
12 The Renaissance of Greek Mathematics and Early Modern Empiricism
âAndré Goddu
Bibliography
Index
Graduate and post-graduate students, as well as university and research scholars specialized in the history of science, philosophy, and mathematics will find this book engaging and rich of new insights into the way mathematics and philosophy interacted before modernity.