During the first few decades of the twentieth century, philosophers
and mathematicians mounted a sustained effort to clarify the nature
of mathematics. This led to considerable discord, even enmity, and
yielded fascinating and fruitful work of both a mathematical and a
philosophical nature. It was one of the most exhilarating
intellectual adventures of the century, pursued at an
extraordinarily high level of acuity and imagination. Its legacy
principally consists of three original and finely articulated
programs that seek to view mathematics in the proper light:
logicism, intuitionism, and finitism. Each is notable for its
symbiotic melding together of philosophical vision and mathematical
work: the philosophical ideas are given their substance by specific
mathematical developments, which are in turn given their point by
philosophical reflection.
This book provides an accessible, critical introduction to these
three projects as it describes and investigates both their
philosophical and their mathematical components.
Solutions manual is available upon request.
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