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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."
This book presents a new approach to the epistemology of
mathematics by viewing mathematics as a human activity whose
knowledge is intimately linked with practice. Charting an exciting
new direction in the philosophy of mathematics, Jose Ferreiros uses
the crucial idea of a continuum to provide an account of the
development of mathematical knowledge that reflects the actual
experience of doing math and makes sense of the perceived
objectivity of mathematical results. Describing a historically
oriented, agent-based philosophy of mathematics, Ferreiros shows
how the mathematical tradition evolved from Euclidean geometry to
the real numbers and set-theoretic structures. He argues for the
need to take into account a whole web of mathematical and other
practices that are learned and linked by agents, and whose
interplay acts as a constraint. Ferreiros demonstrates how advanced
mathematics, far from being a priori, is based on hypotheses, in
contrast to elementary math, which has strong cognitive and
practical roots and therefore enjoys certainty. Offering a wealth
of philosophical and historical insights, Mathematical Knowledge
and the Interplay of Practices challenges us to rethink some of our
most basic assumptions about mathematics, its objectivity, and its
relationship to culture and science.
This is a reproduction of a book published before 1923. This book
may have occasional imperfections such as missing or blurred pages,
poor pictures, errant marks, etc. that were either part of the
original artifact, or were introduced by the scanning process. We
believe this work is culturally important, and despite the
imperfections, have elected to bring it back into print as part of
our continuing commitment to the preservation of printed works
worldwide. We appreciate your understanding of the imperfections in
the preservation process, and hope you enjoy this valuable book.
++++ The below data was compiled from various identification fields
in the bibliographic record of this title. This data is provided as
an additional tool in helping to ensure edition identification:
++++ La Soberbia: (paginas De Todos Los Tiempos) Jose Ferreiro y
Peralta Impr. de Manuel Minuesa, 1866
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