Labyrinth of Thought discusses the emergence and development of
set theory and the set-theoretic approach to mathematics during the
period 1850-1940. Rather than focusing on the pivotal figure of
Georg Cantor, it analyzes his work and the emergence of transfinite
set theory within the broader context of the rise of modern
mathematics. The text has a tripartite structure. Part 1, The
Emergence of Sets within Mathematics, surveys the initial
motivations for a mathematical notion of a set within several
branches of the discipline (geometry, algebra, algebraic number
theory, real and complex analysis), emphasizing the role played by
Riemann in fostering acceptance of the set-theoretic approach. In
Part 2, Entering the Labyrinth, attention turns to the earliest
theories of sets, their evolution, and their reception by the
mathematical community; prominent are the epoch-making
contributions of Cantor and Dedekind, and the complex interactions
between them. Part 3, In Search of an Axiom System, studies the
four-decade period from the discovery of set-theoretic paradoxes to
Godel s independence results, an era during which set theory
gradually became assimilated into mainstream mathematics;
particular attention is given to the interactions between axiomatic
set theory and modern systems of formal logic, especially the
interplay between set theory and type theory. A new Epilogue for
this second edition offers further reflections on the foundations
of set theory, including the "dichotomy conception" and the
well-known iterative conception."
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