INDEX

algebra 64 n 1, 94 algorithm 69 Anima Mundi 24 n 9 Archimedes 33 Aristotelian sense 76 n 7 terminology 126 Aristotle 120 arithmetic 26–27, 64 n 1, 89 atomism 51, 53, 63, 121

Being 8 n 4, 20–21, 86 Bernoulli Jean, 16 n 3, 24 n 9, 34, 41–45, 47–48, 52, 60, 105, 112 n 1 Cantor 16 Carnot 35 n 1, 39, 80, 82, 90, 101–102, 104, 109 n 3, 126 Cartesian(ism) concept 6, 50 mechanism 110, 118 rationalism 66 Cauchy 16 n 2 Cavalieri 50 Chinese language 58 Compagnonnage 129 n 2 Coomaraswamy, A. K. 14 n 14 cosmos 24 n 9, 117 Couturat, L. 10 n 6, 39 n 7, 52 n 9, 64 n 1, 69 n 1, 70 n 3, 84 n 2

denary 58 Descartes 11–12, 19 n 1, 62 equilibrium 57, 75, 86, 96–99

Euclid 79 Europe 3 n 5 evolution 45

Far–Eastern cosmology 98 n 4 tradition 96, 99 fraction(s) 26, 29, 31 n 1, 48–49, 54, 56, 113 n 2 Freycinet, Ch. de 38 n 6, 69 n 2, 71 n 4, 81 n 8, 101, ns 3–4 Galileo 16 n 2 geometry 1, 36, 45, 61, 72, 94, 129 n 2 Grandi, Guido 16 n 3 ‘Great Man’, (Kabbalistic) 45 Greek 3 n 5, 58

Harvey 44 Hebrew 3 n 5 Hegelian affirmation 77 helix 13 n 12 Hermetic figure 6 n 6 ‘coagulation’ and ‘solution’ 97 n 2 Huygens 103 n 1

Indian 3 n 5 individualism 5 Infinity degrees of 41–46 symbol of 86 Kabbalah 2, 3 n 5

Lagrange 81 Leeuwenhoeck 44 Leibnitz 4–6, 9, 11–12, 15–24, 31–53, 60–85, 90, 94, 98 n 3, 100–110, 112 n 1, 118, 122 n 1, 128 Leibnitzian ‘virtuality’ 85 _luz_, Judaic concept of 45

Mallebranche, R. P. 67 n 5 Marquis de l’Hôpital 36 n 4, 79 n 3 mathematician(s) 37, 71–72, 103 mathematics 1, 3–4, 36, 39, 66–67, 89–90, 95, 106–107, 130 metaphysics 10, 20 n 3, 42, 129 Middle Ages 3 n 5, 5, 129 ns 2–3

Newton 5 Nieuwentijt 103 Non–Being 86–87, 99 numbers incommensurable 28–29, 57 n 3 whole 16, 25–28, 54–57, 86, 89, 93–94, 99, 116

ontology 20 n 3, 40

Pascal 39 n 9 physics 36, 61, 67 n 5 physiologists 121 Platonism 1, 14 n 14 principal ‘numerations’ 3 n 5 Pythagorean(s) 1–2, 45, 59

_Quinta Essentia_ 6 n 6

Renouvier 10 n 6, 18 n 5, 63 Rosicrucian 5, 32 n 4 Rota Mundi 6 n 6 Saint Thomas Aquinas 20–21 Scholasticism 11 Scholastic distinction 11 doctrines 5 _secundum quid_ 12 n 8 sense 76 n 7 Scholastics 8, 19–20, 42, 62, 96 Schulenburg 68 n 7 Sephiroth 3 n 5 Spinoza 8 n 2, 18 n 6 stars 33, 44 Stoics 24 n 9

_Tao Te Ching_ 58 _Tetraktys_ 59 theology 129 Trinity 129 n 2

Universal All 7–9, 18 n 6, 22, 24 n 9, 86

Varignon 12 n 11, 16 n 3, 34 ns 6–8, 36 n 3, 41 n 2, 48 n 5, 49 n 6, 66 n 3, 67 n 5, 74 n 2, 75 n 4, 80 n 4

Wallis 16 n 3 Wolf, V. Cl. Christian 74 n 1

_yang_ 98 n 4 _yin_ 98 n 4 Zeno of Elea 120–121 Zero 83–88 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.

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.

The Collected Works of René Guénon brings together the writings of one of the greatest prophets of our time, whose voice is even more important today than when he was alive.

Huston Smith, The World's Religions