David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Cambridge University Press (2013)
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
|Keywords||Logic, Symbolic and mathematical|
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|Call number||QA9.65.S65 2013|
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Citations of this work BETA
Catarina Dutilh Novaes (2011). The Different Ways in Which Logic is (Said to Be) Formal. History and Philosophy of Logic 32 (4):303 - 332.
Cezary Cieśliński & Rafal Urbaniak (2013). Gödelizing the Yablo Sequence. Journal of Philosophical Logic 42 (5):679-695.
Selmer Bringsjord & Naveen Sundar Govindarajulu (2012). Given the Web, What is Intelligence, Really? Metaphilosophy 43 (4):464-479.
Jared Warren (2015). Conventionalism, Consistency, and Consistency Sentences. Synthese 192 (5):1351-1371.
Edgar Andrade-Lotero & Catarina Dutilh Novaes (2012). Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW] Journal of Philosophical Logic 41 (2):387-418.
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