Read more
Mathematics and Philosophy at the Turn of the First Millennium sheds light on Abbo's original philosophical system anchored in two central doctrines, which serve as a compass to navigate it: the theory of oneness (henology) and the theory of composition.
List of contents
IntroductionChapter 1Abbo and His Time: European History and Mathematics
1. Politics and (Religious) Culture
2. Liberal Arts
3. Mathematics
3.1 Speculative Arithmetic
3.2 Practical Arithmetic
Chapter 2Victorious'
Calculus and Abbo's
Explanatio 1. Contents of the
Calculus 1.1
Praefatio de ratione calculi 1.2 Multiplication Tables
1.3 Supplementary Tables and Texts
2. Victorious,
scripulorum calculator: the Calculus and the Reckoning of Time
3. Two Hypothesis on the Arrival of the
Calculus at Fleury
3.1 Hypothesis A: Lupus of Ferrière
3.2 Hypothesis B: Columbanus and the Abbey of Bobbio
4. Abbo's
Explanatio: Manuscripts and Critical Editions
5. Contents of the
Explanatio 5.1 The Prologue (Section I)
5.2 The Theological Premise (Section II)
5.3 The Commentary on on Victorius's
Praefatio (Section III)
5.4 The Commentary on Victoriuous's Multiplication Tables (Section IV)
5.5 On Qualitative Physics (Section V)
6. The Pedagogical Aim and the Role of the Commentator
Chapter 3A Theological Premise: Number, Measure, and Weight
1. Augustine and
Wisd. 11:21
2. Claudianus Mamertus'
De statu animae 3. Arithmetical Readings of
Wisd. 11: 21: Hrabanus Maurus and John Scotus Eriugena
4. Abbo's
Tractatus de numero, mensura et pondereChapter 4Henology
1. Neopythagorean Elements: Unity and the Flow of Numbers
2. The Highest Good,
individuum, and Unity
3. The Lambda Diagram: a Quadrivial Henology
4. Unity as Ontological Principle
5. Unity as the Object of Arithmetic and Calculus
Chapter 5The Composition of Reality
1. Natural Compounds
1.1 The Arithmology of Natural Compounds
1.2 Natural Compounds and Change: the Phases of the Moon
2. Artificial Compounds
2.1 The Five Kinds of Inequality Ratios
2.2 Two
trinae regulae for Arithmetical Ratios
3. Ontological Composition: the Case of the Earth in
Gen. 1:2
4. Division of Non-Material Entities: the Case of the Units of Time
5. Divisibility and Corporality: the Case of the
voxChapter 6Arithmetic and Calculus
1. Fractions: Ounces and
minutiae 2. Representing Integer Numbers
3. Calculus by Fingers or the
loquela digitorum 4. Calculus by Tables
5. Multiplication Rules
Chapter 7Physics Before the
Physics 1. The Early Medieval Concern for Natural Phaenomena
2. Scientific Literature in the Early Medieval Fleury Area
3. Qualitative Physics: from Astronomy to Physiology
4. The Natural Power of Things
Conclusions
About the author
Clelia V. Crialesi is a Marie Sk¿odowska-Curie Fellow at SPHERE-CNRS (France). Formerly, she was an FWO Research Fellow at KU Leuven (Belgium) and a Mellon Fellow at PIMS (Canada). Her research focuses on premodern mathematical thought, with publications ranging from Boethian number theory to Euclidean geometry in the late medieval continuum debate.
Summary
Mathematics and Philosophy at the Turn of the First Millennium sheds light on Abbo’s original philosophical system anchored in two central doctrines, which serve as a compass to navigate it: the theory of oneness (henology) and the theory of composition.
