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An Introduction to Gödel's Theorems (Cambridge Introductions to Philosophy) (Inglés)


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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.

Descripción del libro

An extensively rewritten second edition of this best-selling standard text for graduates and upper-level undergraduate students of logic, philosophy of mathematics, and pure mathematics. A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems.


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Challenging, Compelling, and Overall Very Excellent! 19 de octubre de 2014
Por Desmond Laffan - Publicado en Amazon.com
Formato: Tapa blanda
This book lays out a clear, concise, and yet challenging and compelling introduction to Godel's Incompleteness theorems. The book exhibits a logical succession of chapters so as to ensure ease in understanding the criteria from chapter to chapter, as the material builds and builds upward to a final and cohesive result, that is, Godel's First and Second Theorems. Much of this book is written in the language of formal logic, so some background in logic and proofs is assumed by the author. Peter Smith presents the information intelligently and efficiently, and does not insult the reader's intelligence (which unfortunately occurs in some nonfiction texts). Overall, I have truly enjoyed reading this book, and it is rewarding to stick with diligently. It presents the reader with challenging material and (at least in my opinion) does not hold the reader's hand as they progress and learn. My copy has much wear and tear because it has gone just about everywhere with me. Physically, the book can hold up to wear and tear over time, and I have not had any issues thus far with its durability. If you are looking to acquire strong footing in formal logic, proofs, and most importantly Godel's Theorems as a beginner, I would strongly recommend this book!
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A comment about how the book is printed, not about the content 30 de septiembre de 2013
Por Private Pyle - Publicado en Amazon.com
Formato: Tapa blanda Compra verificada
This may be poorly expressed, but here goes: the text of this book is printed in such a light ink that the contrast between the print and the white background is much diminished. It's not black ink against a white page so much as a gray ink (even a light grey) against a white background. I'm finding the text physically diffiult to read for this reason. What's next, invisible ink?