There's Something About Gödel by Berto

[Aetixintro]

There's Something About Gödel by Francesco Berto is not a book for introduction to Gödel's Incompleteness Theorem!

As it says: "The title takes seriously Ernest Nagel and James R. Newman, who, in their classic book Gödel's Proof, have claimed that such a proof is an "amazing intellectual symphony.""

Another quote: "The second part is thoroughly and unashamedly influenced by Gödel's Theorem: An Incompleteness Guide to Its Use and Abuse" - 2005/Torkel Franzen. I'm heavily sceptical to this kind of book that is best left to people who like to read about Gödel and all its funny contexts.

[Edit, 16.08.2010:] By "heavily sceptical" I mean that application of Gödel's Theorem should be done by certified Logicians and that exposing stupidity (made by others) has very limited use. I've applied some speculation concerning Gödel by asserting "Gödel Incompleteness" for this particular incompleteness and also suggest that Gödel's Theorem (under Phil. of Religion) may suggest the impossibility to get knowledge of God no matter what and that it's reasonable that we don't know God even if God does not exist! Shoot at me all you want, but I'm not serious enough to be criticised in such a book by these two issues until they are dealt with by this certified Logician or these certified Logicians as serious (and valid) claims/concerns. I hope this relieves you of this particular "scepticism" (because I'm not sceptical to the work of Gödel whatsoever unless I can find a good angle to attack from and make it valid/plausible from this certified Logician's point of view, implying that I might become a certified Logician in the far future, hypothetically! [End of edit.]

The book also assumes the knowledge of Typographical Number Theory as it appears in Hofstadter's Gödel, Escher, Bach. So, I guess that it's recommended that one buys both Hofstadter's book and Ernest Nagel and James R. Newman's book.

So I'm disappointed with this book in the way it presents the Gödel's Theorem because I've expected that it would present the logical structure and the logical proof in its entirety and together rather than the scarce logical notation that's spread everywhere in the first part of the book.

So it's half seriousness and half comedy, you can take a look yourself, but for myself, I'll be looking for a better presentation to the G. Theorem and throw a glance to this book to see how this review justifies or needs correction to bow for its virtue. Cheers!

[Richard Baron]

Sorry it wasn't to your taste. I described it as semi-technical when recommending it in your other thread on the topic. Perhaps I should have left out "semi-".

I take the point that it does not set out, in an easily digestible form, the full content of Gödel's theorems. But I fear that one cannot come to a proper grasp of the theorems without grinding through the mathematics. This is one reason why the the theorems, and especially the first one, are so open to misinterpretation and mis-use. People who have not ground through the mathematics imagine that they have got the general idea, and go on to draw extravagant conclusions.

I don't think that the reader need buy extra books. Berto sets out typographical number theory at the start of chapter 3.

[Aetixintro]

Thanks for your reply, Richard Baron!

At least I don't like the set-up in comparison to another excellent Logics book: The Logic Book 4th ed. Bergmann, Moor and Nelson (2004).

I also note that Richard Jeffrey touches on it by his Formal Logic - Its Scope and Limits 3rd ed. (1991).
(Chapter 8 and Chapter 9, specifically)