In 1931, the young Kurt Gödel published his First Incompleteness
Theorem, which tells us that, for any sufficiently rich theory of
arithmetic, there are some arithmetical truths the theory cannot prove.
This remarkable result is among the most intriguing (and most
misunderstood) in logic. Gödel also outlined an equally significant
Second Incompleteness Theorem. How are these Theorems established, and
why do they matter? Peter Smith answers these questions by presenting an
unusual variety of proofs for the First Theorem, showing how to prove
the Second Theorem, and exploring a family of related results (including
some not easily available elsewhere). The formal explanations are
interwoven with discussions of the wider significance of the two
Theorems. This book - extensively rewritten for its second edition -
will be accessible to philosophy students with a limited formal
background. It is equally suitable for mathematics students taking a
first course in mathematical logic.

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