Sextus Empiricus Against the Arithmeticians

Translated with an Introduction and Commentary by Lorenzo Corti

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Author:
Lorenzo Corti
Arithmetic deals with numbers: but what is the nature of their existence, of their parts, and of their relationship with countable items? These questions nourished a lively debate between the Platonico-Pythagorean tradition (trying to answer them) and the Pyrrhonian tradition (trying to show that these answers were unsatisfactory). The debate lies at the heart of Sextus Empiricus’ Against the Arithmeticians. The present book aims at facing the remarkable historical and philosophical questions raised by Sextus’ treatise by offering a new translation of it and the first dedicated commentary to it.
Copyright Year:
2024
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978-90-04-67950-4
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21 Dec 2023
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978-90-04-67949-8
Publication:
19 Dec 2023
Cover Sextus Empiricus <i>Against the Arithmeticians</i>

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Lorenzo Corti (Ph.D. University of Geneva, 2005; HDR University of Lille, 2019) is Lecturer in Ancient Philosophy at the University of Lorraine and Fellow at the Archives Henri-Poincaré. His publications include articles on the nature of Pyrrhonism, on its debates with the Platonic and medical traditions and on Aristotle’s Metaphysics; Scepticisme et langage (Paris, 2009: Prize ʻReinach 2010ʼ); (as editor), τὰ μεταξύ: les Intermédiaires mathématiques chez Aristote, et après, Revue de Philosophie Ancienne (2022).
Acknowledgements

Introduction
 1 Sextus’ Life and Works
 2 Against the Professors: A Glance at Sextus’ Targets, Method, and Sources
 3 Against the Arithmeticians: An Introductory Overview
 4 Originality and Interest of the Present Work
Translation

Commentary

1 M IV 1: Quantities, Number, and Arithmetic
 1 Textual Remarks
 2 Sextus’ Distinction of Continuous and Discrete Quantities and Its Aristotelian Origin
 3 Arithmetic, Philosophy of Number, and Sextus’ Strategy in M IV

2 M IV 2–10: The Derivation System, the Old Academy, and Posidonius
 1 Textual Remarks
 2 Notes on the Translation
 3 What Is the Ultimate Origin of the Dogmatic Doctrine Described in M IV 2–10?
 4 Sextus’ Accounts of the Pythagorean Doctrine at M IV 2–10 and at M IV 92–109, and Posidonius

3 M IV 11–20: Sextus’ Attack on the One
 1 Textual Remarks
 2 The Two ‘Platonic’ Characterisations of the One (M IV 11)
 3 The Argument in Support of the Platonist Conception of the One (M IV 11–13)
 4 The First Cluster of Arguments against the Platonist Conception of the One (M IV 14–18)
 5 The Second Argument against the Platonist Conception of the One (M IV 18–20)

4 M IV 21–2: Sextus’ Attack on the Two
 1 Textual Remarks
 2 Sextus’ Argument against the Number Two: M IV 21–2 in the Light of M X 308–9
 3 The Origin of the Puzzle: Plato, Phaedo 96e–97b, 101 b–c
 4 Number and Generation: PH III 164–5 and M X 323, 328–30

5 M IV 23–30: Sextus’ Attack on Number Conceived of as the Result of the Subtraction of a Unit
 1 Introduction
 2 M IX 311–20 and PH III 88–93
 3 M IV 23–30 in the Light of the loci similes
 4 M IV 24–5: Number, Whole, and Substance

6 M IV 31–4: Sextus’ Attack on Number Conceived of as the Result of the Addition of a Unit
 1 Introduction
 2 M IV 31–2: Number, Units, and Conceptual Parts
 3 M IV 33: Number, Addition, and Generation

Conclusion
Bibliography
Specialists in ancient philosophy (scholars and researchers).
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