Gödel, Kurt On Formally Undecidable Propositions of Principia Mathematica and Related S ystems
Dover Publications 1992 0486669807 / 9780486669809 Paperback Very Good
A copy that has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged. In 1931, a young Austrian mathematician published an epoch-making paper con taining one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic syste m, even in elementary parts of arithmetic, there are propositions which can not be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The reper cussions 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-r eaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge Univers ity}, 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.