On Formally Undecidable Propositions Of Principia Mathematica And Related Systems

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Condition: Very Good. Owners name on front free endpaper. Slight light damage on the back cover. Otherwise excellent. 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 with in the system, is one of the most important contributions to logic since Aristotle. Any formal logical system which disposes of sufficient means to compass the addition and multiplication of positive integers and zero is subject to this limitation. so that one must consider this kind of incompleteness an inherent characteristic of formal mathematics as a whole, which was before this customarily considered the unequivocal intellectual discipline par excellence. This translation, by B. Meltzer, is greatly aided by the introduction by R. B. Braithwaite. This not only points out the significance of Gödel’s work, but illuminates it by a paraphrase of the major part of the whole great argument.