Sextus Empiricus Against the Arithmeticians

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