The continuous and the infinitesimal in mathematics and philosophy
Print Book, English, 2006
Polimetrica, International Scientific Publisher, Milano (Italy), 2006
352 pages : illustrations ; 25 cm
9788876990151, 8876990151
326879360
Introduction
Part I. The continuous, the discrete, and infinitesimal in the history of thought
The continuous and the discrete in Ancient Greece, the Orient, and the European Middle Ages
The 16th and 17th centuries: the founding of the infinitesimal calculus
The 18th and early 19th centuries: the age of continuity
The reduction of the continuous to the discrete
Dissenting voices: divergent conceptions of the continuum
Part II. Continuity and infinitesimals in today's mathematics
Topology
Category/topos theory
Nonstandard analysis
The continuum and constructive and intuitionistic mathematics
Smooth infinitesimal analysis/synthetic differential geometry
Coda