One of the ways contemporary ‘scientism’ encroaches upon metaphysics is through an irresponsible use of such terms as ‘zero’ and ‘infinity’. Mathematics as ‘pure abstraction’ seems to the uninformed like a kind of ‘mystical language’ empowering scientists to unravel the secrets of the universe and to express them in precise terms that allow technicians-whom we like to call ‘wizards’-to transform them into devices of awesome complexity and power.

Guénon agrees with Plato that mathematics can furnish symbols for metaphysics. But it cannot fulfill this function if metaphysical principles in themselves are not understood-which they clearly are not by the vast majority of modern mathematicians and scientists. Guénon sees Leibnitz, discoverer of the infinitesimal calculus and major critic of Descartes, as a significant modern philosopher of mathematics, whose insights are worth placing in a metaphysical context-something Leibnitz himself tried to do. Guénon helps make these efforts more metaphysically intelligible, and transposes them to a higher level. In Metaphysical Principles of the Infinitesimal Calculus, René Guénon points the way toward a rediscovery of mathematics as the handmaiden of metaphysics.

Table of Contents

Chapter 1 Infinite and Indefinite
Chapter 2 The Contradiction of ‘Infinite Number’
Chapter 3 The Innumerable Multitude
Chapter 4 The Measurement of the Continuous
Chapter 5 Questions Raised by the Infinitesimal Method
Chapter 6 ‘Well-Founded Fictions’
Chapter 7 ‘Degrees of Infinity’
Chapter 8 ‘Infinite Division’ or Indefinite Divisibility
Chapter 9 Indefinitely Increasing and Indefinitely Decreasing
Chapter 10 Infinite and Continuous
Chapter 11 The ‘Law of Continuity’
Chapter 12 The Notion of the Limit
Chapter 13 Continuity and Passage to the Limit
Chapter 14 ‘Vanishing Quantities’
Chapter 15 Zero is not a Number
Chapter 16 The Notation of Negative Numbers
Chapter 17 Representation of the Equilibrium of Forces
Chapter 18 Variable and Fixed Quantities
Chapter 19 Successive Differentiations
Chapter 20 Various Orders of Indefinitude
Chapter 21 The Indefinite is Analytically Inexhaustible
Chapter 22 The Synthetic Character of Integration
Chapter 23 The Arguments of Zeno of Elea
Chapter 24 The True Conception of ‘Passage to the Limit’
Chapter 25 Conclusion
Index

[Return to Catalog] - [Fons Vitae titles] - [Sufism] - [Order books] - [Fons Vitae Printable Catalog]

[Rene Guenon Sophia Perennis Series] - [Religious Metaphysics. Art and Symbolism]