Read Online On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel 0800759669806 Books

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In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.
The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.
This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

Read Online On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel 0800759669806 Books

"It is illuminating to read this book."

Product details Series Dover Books on Mathematics Paperback 80 pages Publisher Dover Publications (April 1, 1992) Language English ISBN-10 0486669807

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On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel 0800759669806 Books Reviews :

On Formally Undecidable Propositions of Principia Mathematica and Related Systems Kurt Gödel 0800759669806 Books Reviews

• This book is quite short, but it is also very deep. Kurt Gödel was a mathematician back in the 1930s that had an idea. He grew up during a time where it was thought that everything could be explained through mathematics and that mathematics itself would be "complete." However, Kurt Gödel comes up one fine day in 1931 or so and publishes this little paper explaining that there are ideas that can't be expressed in the language of mathematics. Using the language developed by Bertrand Russell and Alfred North Whitehead, Kurt Gödel establishes basic math and then proceeds to tear it down. A tour de force of logic.
• I wish I had been exposed years ago to the philosophy of mathematics and the inseparableness of mathematics and logic. Seems obvious now. I could blame the education I received and the focus it placed on how instead of why. But perhaps that’s too easy an excuse and the why was always there and I was too immature to see it. Either way, it’s a good read...
• This is not a simple read for non-mathematicians, but it is outstanding due to the extended explanatory introduction for others with backgrounds in natural sciences, logical, or philosophical matters.
• It is illuminating to read this book.
• THE proof as Goedel wrote it (plus typos). I have seen modern proofs of this theorem which are much easier to follow (as an example, a Mir book on mathematical logic by a Russian mathematician whose name I cannot recall), but this one is the REAL thing.
  Modern proofs can be much clearer, but the original always has an added value. The writing style is not the best, but by reading this version you get a clearer idea of how Goedel came up with his theorem and the many difficulties he faced. Remember, by the time most of us read or heard about this for the first time, mathematical logic had advanced quite a few decades.
• I had to read it a few times but I thought it was worth reading.
• Writing doesn't matter. This is a must for everyone in foundatoins.
• In my humble opinion one of the most important discoveries of the 20th century. In fact it means that to describe the world with a consistent and complete logical theory, we need an infinit number of hypothesis!