After the overviews, he takes on various applications/misapplications of the theorems by topic. With that said, I still think it is quite worthwhile reading, and at a slim 170ish pages, it is a fairly quick read. The overviews will also seem a bit alien to someone expecting and Nagel & Newman kind of treatment instead, this is discussed from a more abstract perspective of the characteristics and properties of formal systems, which avoids getting into the gritty details (even Gödel-numbering is not explained in detail!) but may be hard to grasp for someone not used to thinking at this level of abstraction about mathematical systems. The overviews of the theorems themselves is not as lucid as I imagine they could be (which is why I rate it a 4 instead of a 5). The book is however, largely free of formulas and proofs, for those who are dissuaded by such. 10 he talking about Diophantine equations and Goldbach-like conjectures, and soon after, "PA" and "ZFC" are tossed about as if they were practically everyday acronyms for most people. As evidenced from the title, the primary focus of the book is to identify the specific nature of these theorems, where they apply directly, and where they do not apply directly, and where they are interpreted entirely erroneously.Īlthough the book is aimed at non-mathematicians and those with no knowledge of formal logic, I can't really imagine someone with no understanding of logic and some fair amount of math comprehension benefitting alot from this book.
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