Jeffrey, Computability and Logic (CUP, 3rd edn 1989). Epstein and Walter A Carnielli, Computability: Computable functions, logic, and the foundations of mathematics (Wadsworth, 3rd edn 2008). The obvious two recommendations, apart from the Smullyan book just mentioned, have to be

I’m reading/have just read IGT and would like some parallel reading at about the same level. Raymond Smullyan, Gödel’s Incompleteness Theorems (OUP, 1992).Ĥ. Or, if you are a bit more mathematical and can cope with a certain degree of terse elegance, there is the simply wonderful Well, there are my own notes (which at least are both a lot shorter and a lot cheaper than IGT, but unsurprisingly run along very similar lines) What if I want more detail that Franzen gives, but still something a lot shorter than IGT? Raymond Smullyan, Forever Undecided: A Puzzle Guide to Gödel (OUP pbk 1998).ģ. A different approach, which some will love, is to be found in one of Smullyan’s classic books exploring logic through puzzles: Franzen is also excellent at pouring cold water on some ludicrous abuses/misinterpretations of Gödel’s result. Which explains the incompleteness theorems and how they are proved, and gives some indication of why they might matter. Torkel Franzen, Gödel’s Theorem: An Incomplete Guide to its Use and Abuse (A.K. But if you want/need a slower introduction, you probably won’t do better than the excellent and rightly much admired There are a lot of symbols in IGT! What should I read if I want something shortish but reliable that will just give me some headline news without all the hard work?Īs so often, the Stanford Encyclopedia of Philosophy is a good place to start: the entry on Kurt Gödel by Juliette Kennedy gives a brisk account of the incompleteness theorems, and then there is of course lots more in the entry specifically on Gödel’s Incompleteness Theorems by Panu Raatikainen (though there a quite a few symbols there too).

But better, check out the Teach Yourself Logic Guide for suggestions for elementary logical reading.Ģ.

I suppose you could try reading IGT and filling in logical background (from Wikipedia, for example) on a need-to-know basis. But you don’t need very much background: a reading knowledge of standard logical symbolism, the idea of a formal system for first-order logic, the ideas of soundness and completeness, the idea of a formal axiomatized theory … I am afraid that you do need some logical background to tackle my book (and likewise for most alternative presentations). What do I need to know before I can read IGT? So here are some suggestions, for different kinds of audiences.ġ. I’m sometimes asked for recommendations about what to read before or after IGT - or indeed, what to read instead of tackling IGT if you are looking for something less weighty, or alternatively looking for something more like a conventional mathematical text.

Gödel's Theorem by Torkel Franzén