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Akribeia: Certainty and Ontology of Mathematics in Alessandro Piccolomini's De certitudine mathematicarum
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This book provides a comprehensive study of the origins of seminal early modern debates on the certainty and ontology of mathematics. It analyzes Alessandro Piccolomini’s
De certitudine mathematicarum (1547), a work that ignited widespread controversy by challenging the scientific status of mathematics. The study delves into Piccolomini’s logical doctrines, his philosophy of mathematics, and his perspectives on the relationship between mechanics and natural philosophy. Special attention is given to Piccolomini’s ancient and medieval sources, the 16th-century rediscovery of Proclus’
In Euclidem, and the influence of Priscian’s
In De Anima.
Álvaro José Campillo Bo, Ph.D. (2023), University College Dublin, studies the early modern Latin reception of the Neoplatonic philosophy of mathematics and the ensuing epistemological, metaphysical, and scientific debates it provoked.
Acknowledgements
List of Figures and Tables
1 Introduction
1.1 Mathematical Akribology: a Perennial Question
1.2 Piccolomini’s Intellectual Background to De certitudine
1.3 De certitudine Mathematicarum: Themes and Hermeneutical Keys
1.4 State of the Art
1.5 Reassessing Piccolomini’s Text
1.6 The Map of This Book
2 Piccolomini’s Sources and Context
2.1 Proclus in the Latin Context and Neoplatonic Themes in De certitudine
2.2 Phantasia: Ontology and Epistemology
2.3 Certitudo mathematica: a Historical Inquiry
2.4 Anti-mathematical Attitudes in the 16th-Century Italian Context
2.5 Pseudo-Aristotle’s Quaestiones mechanicae
2.6 Demonstratio potissima
3 De Certitudine Mathematicarum
3.1 Piccolomini’s demonstratio potissima: a Truncated regressus
3.2 Mathematical Analysis and demonstratio potissima
3.3 Euclid’s I.32: Formal Flaws of Mathematical Demonstration
3.4 Quasi παράδοξον: Piccolomini’s Denial of Mathematical Causality
3.5 Piccolomini’s Philosophy of Mathematics
3.6 Mathematising the Unmathematical: Back to the Mertonian Challenge
3.7 Common Mathematics and De certitudine’s Consistency: a Hypothesis
Conclusions
Appendix
Bibliography
Manuscripts
Primary Sources
Secondary Sources
Index of Manuscripts
Index of Ancient Authors
Index of Modern Authors
List of Figures and Tables
1 Introduction
1.1 Mathematical Akribology: a Perennial Question
1.2 Piccolomini’s Intellectual Background to De certitudine
1.3 De certitudine Mathematicarum: Themes and Hermeneutical Keys
1.4 State of the Art
1.5 Reassessing Piccolomini’s Text
1.6 The Map of This Book
2 Piccolomini’s Sources and Context
2.1 Proclus in the Latin Context and Neoplatonic Themes in De certitudine
2.2 Phantasia: Ontology and Epistemology
2.3 Certitudo mathematica: a Historical Inquiry
2.4 Anti-mathematical Attitudes in the 16th-Century Italian Context
2.5 Pseudo-Aristotle’s Quaestiones mechanicae
2.6 Demonstratio potissima
3 De Certitudine Mathematicarum
3.1 Piccolomini’s demonstratio potissima: a Truncated regressus
3.2 Mathematical Analysis and demonstratio potissima
3.3 Euclid’s I.32: Formal Flaws of Mathematical Demonstration
3.4 Quasi παράδοξον: Piccolomini’s Denial of Mathematical Causality
3.5 Piccolomini’s Philosophy of Mathematics
3.6 Mathematising the Unmathematical: Back to the Mertonian Challenge
3.7 Common Mathematics and De certitudine’s Consistency: a Hypothesis
Conclusions
Appendix
Bibliography
Manuscripts
Primary Sources
Secondary Sources
Index of Manuscripts
Index of Ancient Authors
Index of Modern Authors
The book will be of interest to scholars and students in early modern philosophy, history of mathematics and logic, Neoplatonism, epistemology and theory of science, and Renaissance intellectual history.