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ISBN:0486669807
Author: Kurt Gödel
ISBN13: 978-0486669809
Title: On Formally Undecidable Propositions of Principia Mathematica and Related Systems
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ePUB size: 1888 kb
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Language: English
Category: Mathematics
Publisher: Dover Publications (April 1, 1992)
Pages: 80

On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel



Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Dated November 17, 1930, it was originally published in German in the 1931 volume of Monatshefte für Mathematik. Several English translations have appeared in print, and the paper has been included in two collections of classic mathematical logic papers.

It is very hard to find faults in what may be the most famous proof of the 20th century. For those not familiar with the Russell-Whitehead Principia Mathematica notation this is a very hard book. I had the benefit of the Kac-Ulam explanation. I did find what might be problems with this proof. 1) One is the reliance on number theory proofs about prime numbers that are assumed true in the Gödelization of the primes coding of the mathematical axioms. 2) The second is the assumption that the axioms statements represent the minimal representation of such a system of axioms

On Formally Undecidable Propositions. OfPrincipia Mathematica And Related Systems. KURT GÖDEL Translated by B. MELTZER Introduction by B. BRAITHWAITE. DOVER PUBLICATIONS, INC. New York. son, abridged and repubblication of the work. First published by Busici. in the Un. Pubblications, Inc East 2nd Street, Minest. der Principia Mattiemater opositions of Frincipia mathematice and. relaied systems Kurt Godel Iranslanod by B. tion by R. B Brantit. entitled Uber for. der. Frincipia Mathematica und verwanden.

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.

First English translation of revolutionary paper (1931) that established that 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. Introduction by R. B. Categories: Other Social Sciences\Philosophy. Pages: 79. ISBN 10: 0486669807.

Lists with This Book. Kurt Gödel was a genius and his paper is proof of that fact. I read this book in 2011 and four years later I have come to realize it's probably one of the top ten most influential books I've ever read (not that I have a list).

On Formally Undecidable Propositions. of Principia Mathematica And Related Systems. Translated by B. MELTZER Introduction by R. To christopher fernau. Kurt Gödel’s astonishing discovery and proof, published in 1931, that even in elementary parts of arithmetic there exist propositions which cannot be proved or disproved within the system, is one of the most important contributions to logic since Aristotle

Kurt Gödel’s astonishing discovery and proof, published in 1931, that even in elementary parts of arithmetic there exist propositions which cannot be proved or disproved within the system, is one of the most important contributions to logic since Aristotle  . This paper, entitled "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I (On formally undecidable propositions of Principia Mathematica and related systems I"), is translated in this book.

Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I" ("On Formally Undecidable Propositions of Principia Mathematica and Related Systems I") is a paper in mathematical logic by Kurt Gödel. Because the method of Gödel numbering was novel, and to avoid any ambiguity, Gödel presented a list of 45 explicit formal definitions of primitive recursive functions and relations used to manipulate and test Gödel numbers. He used these to give an explicit definition of a formula Bew(x) that is true if and only if x is the Gödel number of a sentence φ and there exists a natural number that is the Gödel number of a proof of φ. The name of this formula derives from Beweis, the German word for proof.

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. 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.

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.

Reviews: 7
huckman
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.
Mayno
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.
Feri
It is illuminating to read this book.
anonymous
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.
Kiaile
I had to read it a few times but I thought it was worth reading.
Neol
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!
Jonariara
Writing doesn't matter. This is a must for everyone in foundatoins.
good