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