An Incomplete Guide to its Use and Abuse is an extended and self-contained exposition of the incompleteness theorems and a discussion of what informal consequences can, and in particular cannot, be drawn from them. On the heels of Franzén’s fine technical exposition of Gödel’s incompleteness theorems and related topics comes this survey of the incompleteness theorems aimed at a general audience. A brief excerpt from a forthcoming review in History and Philosophy of Logic: An Incomplete Guide to its Use and Abuse (A K Peters, 2005). He has a book out last year in the ASL’s Lecture Notes in Logic series, which is an excellent technical treatment, and now a fine popular book: Gödel’s Theorem. Torkel Franzén has been tireless for at least 15 years in correcting misunderstandings relating to logic on sci.logic (which was a lot of fun in the pre-AOL days), on FOM, and elsewhere. Don’t you wish someone would write a book that catalogs all the various ways in which one can misstate, misunderstand, and misapply Gödel’s theorems, and how to correct such misunderstandings? A book that you can send your students off to read when they say stuff like, “Gödel showed that there is no mathematical truth,” or “The mind can go outside the system, but no formal system can because of incompleteness, so the mind is not a formal system.” Well, it’s here.
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