On Formally Undecidable Propositions of Principia Mathematica and Related Systems

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Courier Dover Publications, 1992 - Mathematics - 72 pages
10 Reviews

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.

  

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Review: On Formally Undecidable Propositions of Principia Mathematica and Related Systems

User Review  - Mitch Allen - Goodreads

The classic math destroying argument presented in the original proofs. The implication of this work is far more interesting to me than the proofs themselves, but it's a powerful work. Read full review

Review: On Formally Undecidable Propositions of Principia Mathematica and Related Systems

User Review  - sologdin - Goodreads

Snarky assholes should present these arguments to their seventh grade algebra teachers: but this is all impossible! why bother? formal axiomatics is undecidable! Read full review

Selected pages

Contents

Chapter 1
37
Chapter 2
41
Chapter 3
63
Chapter 4
69
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About the author (1992)

Kurt Godel was probably the most outstanding logician of the first half of the twentieth century. Born in Czechoslovakia, Godel studied and taught in Vienna and then came to the United States in 1940 as a member of the Institute for Advanced Study at Princeton University. In 1953 he was made a professor at the institute, where he remained until his death in 1978. Godel is especially well known for his studies of the completeness of logic, the incompleteness of number theory, the consistency of the axiom of choice and the continuum hypothesis. Godel is also known for his work on constructivity, the decision problem, and the foundations of computation theory, as well as his views on the philosophy of mathematics; especially his support of a strong form of Platonism in mathematics.

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