An Introduction to Gödel's Theorems

Bibliographic Data

ID23798716
AuthorsPeter Smith (0000-0003-0058-7588), Peter J Smith (0000-0001-8707-2581, University of Cambridge, corresponding author)
Year2001
Publication date2001-01-01
Open AccessYes
TypeBOOK
VenueIntroduction to Gödel's Theorems (SOURCE_BOOK)
PublisherCambridge University Press (PUBLISHER • US)
DOI10.1017/cbo9780511800962
OpenAlexW1554288449
ISBN9780511800962
Open LibraryOL34475897M
LanguageEN
Citations received5

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 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.

Algebra over a field · Algorithm · Arithmetic function · Calculus (dental) · Discrete mathematics · Epistemology · Formal system · Gödel · Gödel's incompleteness theorems · Mathematical logic · Mathematical practice · Mathematical proof · Mathematics education · Programming language · Pure mathematics · Variety (cybernetics) · Computer Science · History and Theory of Mathematics · Mathematical and Theoretical Analysis · Mathematics · Philosophy · Philosophy and Theoretical Science

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