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René Guénon

The Metaphysical Principles of the Infinitesimal Calculus (Collected Works of Rene Guenon) Paperback – 9 Jun. 2004

by René Guénon (Author)

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Guénon'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, Guénon 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 Guénon, 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.

Print length

152 pages
Language

English
Publication date

9 Jun. 2004
Dimensions

15.24 x 0.89 x 22.86 cm
ISBN-10

0900588128
ISBN-13

978-0900588129
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About the Author

René Guénon (1886–1951) was one of the great luminaries of the twentieth century, whose critique of the modern world has stood fast against the shifting sands of intellectual fashion. His extensive writings, now finally available in English, are a providential treasure-trove for the modern seeker: while pointing ceaselessly to the perennial wisdom found in past cultures ranging from the Shamanistic to the Indian and Chinese, the Hellenic and Judaic, the Christian and Islamic, and including also Alchemy, Hermeticism, and other esoteric currents, they direct the reader also to the deepest level of religious praxis, emphasizing the need for affiliation with a revealed tradition even while acknowledging the final identity of all spiritual paths as they approach the summit of spiritual realization. René Guénon, of whom Jacob Needleman wrote in The Sword of Gnosis that ‘no other modern writer has so effectively communicated the absoluteness of truth,’ is gradually being recognized by deeper thinkers as one of the few who have truly penetrated the seductive veil of the modern age. As an expositor of pure metaphysics and its application to the science of symbols, Guénon is without peer; and his extraordinarily prescient critique of the modern world is attracting more and more attention among cultural commentators. Little known in the English-speaking world till the recent appearance of his Collected Works in translation, Guénon has nevertheless long been recognized as a veritable criterion of truth by a vanguard of remarkable writers who evince that rare combination: intellectuality and spirituality. After a lonely childhood, often interrupted by ill health, Guénon navigated the seductive half-truths of occultism toward a deeper, unified vision offering a way out from the confusion and fragmentation of our time. Regarded by leading scholars as the first truly authentic interpreter of many Eastern doctrines in the West, Guénon never tired, in face of the seemingly inexorable process of dissolution in the twentieth century, of pointing to the transcendent unity of all religious faiths and the abiding Truth that contains them all.

Product details

Publisher ‏ : ‎ Sophia Perennis (9 Jun. 2004)
Language ‏ : ‎ English
Paperback ‏ : ‎ 152 pages
ISBN-10 ‏ : ‎ 0900588128
ISBN-13 ‏ : ‎ 978-0900588129
Dimensions ‏ : ‎ 15.24 x 0.89 x 22.86 cm

Best Sellers Rank: 971,585 in Books (See Top 100 in Books)
- 988 in Mathematical Analysis (Books)
- 3,372 in Popular Science Maths
- 15,182 in Christian Living (Books)

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4.7 22 ratings

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George

Excellent

Reviewed in the United Kingdom on 18 November 2019

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A most profound study, although slightly different in character than the rest of his works (as said in the Preface - a rather 'specialist' one).

Reviewed in the United Kingdom on 4 January 2015

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Very Good!

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Ontological Investigations

Number is not Ontology

Reviewed in the United Kingdom on 22 August 2012

In my opinion this is one of the author's most under-regarded books. One of the factors which distinguished Guenon from his contemporaries was his analytical rigour: within his field he was every bit as dispassionate and logical as Frege or Russell (it ought to be remembered that he trained as a mathematician). While this coldness of temperament did lead him to play down and sometimes misinterpret the importance of personal mystic experience and the place of the individual in metaphysics, it meant he was uniquely placed to combat the rising misuse of mathematical terminology in philosophy.

To put that last remark in context I shall proffer an example: it has been over one hundred years since Georg Cantor created his Set Theory, a mathematical system which he believed allowed one to work with 'infinite' number and even multiple 'infinites', 'infinites' of them. The notion of an 'infinite' Set, and indeed the Set Theory as a whole, attracted criticism from its very birth coming under attack from philosophers and metaphysicians of various schools including Ludwig Wittgenstein, and has been largely replaced with mathematical Constructivism: never-the-less certain individuals continue to employ it for dubious ends. Unlike its founder, who preferred to use the term 'Transfinite' to distinguish between his 'infinite' sets and the 'infinity' of the Absolute, subsequent mathematics disregarded this distinction which has lead various Post-Modern philosophers, most prominently Alain Badiou, attempting to use it to disprove the possibility of God and other metaphysical concepts. This book is a vaccine against just such malpractice.

Guenon ruthlessly attacks the notion of a mathematical infinite, arguing than an infinite number is a contradiction in terms. With this aim he surveys the history of modern mathematics, with a particular focus on the Infinitesimal Calculus and the mathematical endeavours of Leibnitz, among others. I say 'among others' for the title, aside from being almost stereotypically 'academic' and dry, is actually rather misleading: as the French metaphysician treats a number of other mathematical subjects of equal if not more importance. Amongst these highlights include the demystification of Irrational Numbers, the axiomic realisation that Negative Numbers are a case of geometry transferred to the mathematical plane and a commentary on the metaphysical property of the Number Zero which one soon realises has a great baring on concepts such as Creatio Ex Nihilo (the apparent opposition between Christianity and the Kabbalah on this point disappears).

I give this volume four stars, not because it's unworthy of a five star review in itself, but because it could have been so much more. Guenon was occupied with his new life in Egypt at the time he wrote the volume, so he can be forgiven for not undertaking a massive project, but if only he had bided his time and if he had but expanded the book's remit! Had he devoted more pages to attacking the above mentioned theories of Cantor directly, as well as turning his attention to the as yet still young British school of Analytical Philosophy which was to play so much a part in the popularisation of Logical Positivism, this book alone would have been enough to ensure his reputation. Never-the-less it is a most excellent book, disrobing modern mathematics of the almost superstitious awe it inspires in the post-Einsteinian era. To lift a quote from the text itself: `The science of Mathematics should be a science of the obvious, yet is currently veiled in an impenetrable cloud and thrusts the onlooker into a labyrinth of paradoxes, each more bizarre than the last'.

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Viola6677

Abstract but enlightening

Reviewed in the United Kingdom on 12 May 2021

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Very abstract, but made me think about many mathematical concepts I usually take for granted.

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