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Gottlob Frege: Basic Laws of Arithmetic (Paperback)
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Gottlob Frege: Basic Laws of Arithmetic (Paperback)
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This is the first complete English translation of Gottlob Frege's
Grundgesetze der Arithmetik (originally published in two volumes,
1893 and 1903), with introduction and annotation. The importance of
Frege's ideas within contemporary philosophy would be hard to
exaggerate. He was, to all intents and purposes, the inventor of
mathematical logic, and the influence exerted on modern philosophy
of language and logic, and indeed on general epistemology, by the
philosophical framework within which his technical contributions
were conceived and developed has been so deep that he has a strong
case to be regarded as the inventor of much of the agenda of modern
analytical philosophy itself. Two of Frege's three principal books
- the Begriffsschrift (1879) and Grundlagen der Arithmetik (1884) -
have been available in English translation for many years, as have
all the most important of his other, article-length writings.
Grundgesetze was to have been the summit of Frege's life's work - a
rigorous demonstration of how the fundamental laws of the classical
pure mathematics of the natural and real numbers could be derived
from principles which, in his view, were purely logical. A letter
received from Bertrand Russell shortly before the publication of
the second volume made Frege realise that Axiom V of his system,
governing identity for value-ranges, led to contradiction. But much
of the main thrust of Frege's project can be salvaged. The
continuing importance of the Grundgesetze lies not only in its
bearing on issues in the foundations of mathematics but in its
model of philosophical inquiry. Frege's ability to locate the
essential questions, his integration of logical and philosophical
analysis, and his rigorous approach to criticism and argument in
general are vividly in evidence in this, his most ambitious work.
General
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