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The Metaphysical Principles of the Infinitesimal Calculus (New)
by Guenon, Rene
Publisher: Sophia Perennis
Book ID: 9780900588129, 0900588128
Guenon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet thread throughout his doctrinal studies. In this late text published just five years before his death, Guenon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path. This book therefore extends and complements the geometrical symbolism he employs in other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. According to Guenon, the concept 'infinite number' is a contradiction in terms. Infinity is a metaphysical concept at a higher level of reality than that of quantity, where all that can be expressed is the indefinite, not the infinite. But although quantity is the only level recognized by modern science, the numbers that express it also possess qualities, their quantitative aspect being merely their outer husk. Our reliance today on a mathematics of approximation and probability only further conceals the 'qualitative mathematics' of the ancient world, which comes to us most directly through the Pythagorean-Platonic tradition.
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.
Guenon 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. Guenon 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. Guenon helps make these efforts more metaphysically intelligible, and transposes them to a higher level. In Metaphysical Principles of the Infinitesimal Calculus, Rene Guenon points the way toward a rediscovery of mathematics as the handmaiden of metaphysics.
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