An Introduction to Gödel's Theorems /
Smith, Peter,
An Introduction to Gödel's Theorems / Peter Smith. - 2nd ed. - 1 online resource (406 pages) : digital, PDF file(s). - Cambridge Introductions to Philosophy . - Cambridge Introductions to Philosophy. .
Title from publisher's bibliographic system (viewed on 04 Apr 2016).
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.
9781139149105 (ebook)
Gödel, Kurt
Logic, Symbolic and mathematical
QA9.65 / .S65 2013
511.3
An Introduction to Gödel's Theorems / Peter Smith. - 2nd ed. - 1 online resource (406 pages) : digital, PDF file(s). - Cambridge Introductions to Philosophy . - Cambridge Introductions to Philosophy. .
Title from publisher's bibliographic system (viewed on 04 Apr 2016).
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.
9781139149105 (ebook)
Gödel, Kurt
Logic, Symbolic and mathematical
QA9.65 / .S65 2013
511.3