The Metaphysical Principles of the Infinitesimal Calculus

Published: 1946

This work aims to clarify and explain the notions underlying the infinitesimal calculus, addressing the misconceptions and lack of principles in modern mathematics. It emphasizes the distinction between the metaphysical Infinite and the mathematical infinite, advocating for a deeper understanding of mathematical concepts rooted in traditional metaphysics.

01PREFACE 02INFINITE AND INDEFINITE 032 THE CONTRADICTION OF 'INFINITE NUMBER'043 THE INNUMERABLE MULTITUDE 054 THE MEASUREMENT OF THE CONTINUOUS 065 QUESTIONS RAISED BY THE INFINITESIMAL METHOD 076 'WELL-FOUNDED FICTIONS'08'DEGREES OF INFINITY'09'INFINITE DIVISION' OR INDEFINITE DIVISIBILITY 10INDEFINITELY INCREASING; INDEFINITELY DECREASING 11THE INFINITE AND THE CONTINUOUS 12THE 'LAW OF CONTINUITY'13THE NOTION OF THE LIMIT 14CONTINUITY AND PASSAGE TO THE LIMIT 15'VANISHING QUANTITIES'16ZERO IS NOT A NUMBER 17THE NOTATION OF NEGATIVE NUMBERS 18REPRESENTATION OF THE EQUILIBRIUM OF FORCES 19VARIABLE AND FIXED QUANTITIES 2019 SUCCESSIVE DIFFERENTIATIONS 21VARIOUS ORDERS OF INDEFINITUDE 2221 THE INDEFINITE IS ANALYTICALLY INEXHAUSTIBLE 2322 THE SYNTHETIC CHARACTER OF INTEGRATION 2423 THE ARGUMENTS OF ZENO OF ELEA 2524 THE TRUE CONCEPTION OF 'PASSAGE TO THE LIMIT'2625 CONCLUSION

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