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Labyrinth of thought

A History of Set Theory and Its Role in Modern Mathematics

Auteurs

José Ferreirós Domínguez

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466pages
17 heures de lecture

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The text explores the emergence and development of set theory and its mathematical approach from 1850 to 1940, contextualizing Georg Cantor's work within the broader evolution of modern mathematics. It is structured in three parts. Part 1, "The Emergence of Sets within Mathematics," examines the initial motivations for a mathematical notion of sets across various disciplines, highlighting Riemann's influence on the acceptance of set theory. Part 2, "Entering the Labyrinth," focuses on the earliest theories of sets, their evolution, and the mathematical community's reception, emphasizing the significant contributions of Cantor and Dedekind and their complex relationship. Part 3, "In Search of an Axiom System," analyzes the four decades following the discovery of set-theoretic paradoxes up to Gödel’s independence results, detailing how set theory became integrated into mainstream mathematics. This section pays special attention to the relationship between axiomatic set theory and modern formal logic, particularly the connections between set theory and type theory. The new Epilogue in the second edition offers additional insights into the foundations of set theory, including the "dichotomy conception" and the iterative conception.