The Metaphysical Principles of the Infinitesimal Calculus
Published: 1946
An examination of the philosophical and metaphysical foundations of the infinitesimal calculus, exploring the concepts of infinity, continuity, and the mathematical infinite.
Chapters
Ch. 0
Preface
Ch. 1
Infinite and Indefinite
Ch. 2
The Contradiction of 'Infinite Number'
Ch. 3
The Innumerable Multitude
Ch. 4
The Measurement of the Continuous
Ch. 5
Questions Raised by the Infinitesimal Method
Ch. 6
'Well-Founded Fictions'
Ch. 7
'Degrees of Infinity'
Ch. 8
'Infinite Division' or Indefinite Divisibility
Ch. 9
Infinite and Continuous
Ch. 10
The 'Law of Continuity'
Ch. 11
The Notion of the Limit
Ch. 12
Continuity and Passage to the Limit
Ch. 13
'Vanishing Quantities'
Ch. 14
Zero is not a Number
Ch. 15
The Notation of Negative Numbers
Ch. 16
Representation of the Equilibrium of Forces
Ch. 17
Variable and Fixed Quantities
Ch. 18
Successive Differentiations
Ch. 19
Various Orders of Indefinitude
Ch. 20
The Indefinite is Analytically Inexhaustible
Ch. 21
The Synthetic Character of Integration
Ch. 22
The Arguments of Zeno of Elea
Ch. 23
The True Conception of 'Passage to the Limit'
Ch. 24