Book contents
- The Ladder of the Sciences in Late Antique Platonism
- Cambridge Texts and Studies In Platonism
- The Ladder of the Sciences in Late Antique Platonism
- Copyright page
- Contents
- Tables and Charts
- Preface
- Acknowledgements
- Introduction
- Part I Rhetoric as an Instrument of Philosophy
- Part II Ethics
- Part III Political Science
- Part IV Mathematics
- Chapter 21 Mathematics and the Sciences in Proclus
- Chapter 22 The Music of Philosophy in Late Antiquity
- Chapter 23 The Music of the Virtues in Late Antique Platonism
- Chapter 24 Hearing the Harmony of the Spheres in Late Antiquity
- Part V Metaphysics
- Postscript
- Bibliography
- Index Locorum
- General Index
Chapter 21 - Mathematics and the Sciences in Proclus
from Part IV - Mathematics
Published online by Cambridge University Press: 08 December 2025
Book contents
- The Ladder of the Sciences in Late Antique Platonism
- Cambridge Texts and Studies In Platonism
- The Ladder of the Sciences in Late Antique Platonism
- Copyright page
- Contents
- Tables and Charts
- Preface
- Acknowledgements
- Introduction
- Part I Rhetoric as an Instrument of Philosophy
- Part II Ethics
- Part III Political Science
- Part IV Mathematics
- Chapter 21 Mathematics and the Sciences in Proclus
- Chapter 22 The Music of Philosophy in Late Antiquity
- Chapter 23 The Music of the Virtues in Late Antique Platonism
- Chapter 24 Hearing the Harmony of the Spheres in Late Antiquity
- Part V Metaphysics
- Postscript
- Bibliography
- Index Locorum
- General Index
Summary
Only two complete works on the philosophy of mathematics survive from Antiquity, Iamblichus’ De communi mathematica scientia and Proclus’ commentary on Euclid’s Elements Book I. Chapter 21 lists works by Proclus concerning mathematics and the sources he used in these works. Concentrating on Proclus’ commentary on Euclid, I describe his conception of the ontological status of the objects with which mathematics is concerned: these objects are originally concepts innate in human soul, forming part of its very nature, concepts which the mathematician then seeks to articulate, project, construct through various methods so as to constitute an elaborated science. I present also the distinctions made between the mathematical sciences and their methods, the importance of mathematics for other sciences (both superior and inferior to it), and Proclus’ relations with other mathematicians of his time.
Information
- Type
- Chapter
- Information
- The Ladder of the Sciences in Late Antique PlatonismSelected Essays, pp. 277 - 293Publisher: Cambridge University PressPrint publication year: 2026
Accessibility standard: Inaccessible, or known limited accessibility
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
The PDF of this book is known to have missing or limited accessibility features.
We may be reviewing its accessibility for future improvement, but final compliance is
not yet assured and may be subject to legal exceptions. If you have any questions,
please contact
accessibility@cambridge.org.
Content Navigation
Table of contents navigation
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Allows you to navigate directly to chapters, sections, or non‐text items through a linked table of contents, reducing the need for extensive scrolling.
Index navigation
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Provides an interactive index, letting you go straight to where a term or subject appears in the text without manual searching.
Reading Order & Textual Equivalents
Single logical reading order
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
You will encounter all content (including footnotes, captions, etc.) in a clear, sequential flow, making it easier to follow with assistive tools like screen readers.
Short alternative textual descriptions
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
You get concise descriptions (for images, charts, or media clips), ensuring you do not miss crucial information when visual or audio elements are not accessible.
Visual Accessibility
Use of colour is not sole means of conveying information
You will still understand key ideas or prompts without relying solely on colour, which is especially helpful if you have colour vision deficiencies.
You will still understand key ideas or prompts without relying solely on colour, which is especially helpful if you have colour vision deficiencies.
Structural and Technical Features
ARIA roles provided
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.
You gain clarity from ARIA (Accessible Rich Internet Applications) roles and attributes, as they help assistive technologies interpret how each part of the content functions.