Ulteriori informazioni
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.
Sommario
Infinite & indefinite -- The contradiction of 'infinite number' -- The innumerable multitude -- The measurement of the continuous -- Questions raised by the intinitesimal method -- The 'well-founded fictions' -- 'Degrees of infinity' -- 'Infinite division' or indefinite divisibility -- Indefinitely increasing & indefinitely decreasing -- Infinite & continuous -- The 'law of continuity' -- The notion of the limit -- Continuity & passage to the limit -- The 'vanishing quantities' -- Zero is not a number --The notation of negative numbers -- Representation of the equilibrium of forces -- Variable & fixed quantities -- Successive differentiations -- Various orders of indefinitude -- The indefinite is analytically inexhaustible -- The synthetic character of integration -- The arguments of Zeno of Elea -- The true conception of 'passage to the limit'.
