Juliette Kennedy, Gödel’s Incompleteness Theorems

I was in the CUP Bookshop the other day, and saw physical copies of the Elements series for the first time. I have to say that the books are suprisingly poorly produced, and very expensive for what they are. I suspect that the Elements are primarily designed for online reading; and I certainly won’t be buying physical copies.

I’ve now read Juliette Kennedy’s contribution on Gödel’s Incompleteness Theorems. Who knows who the reader is supposed to be? It is apparently someone who needs the notion of a primitive recursive function explained on p. 11, while on p. 24 we get a hard-core forcing argument to prove that “There is no Borel function F(s) from infinite sequences of reals to reals such that if ran(s) = ran(s’), then F(s) = F(s’), and moreover F(s) is always outside ran(s)” (‘ran’ isn’t explained). This is just bizarre. What were the editors of this particular series thinking?

Whatever the author’s strengths, they don’t include the knack of attractive exposition. So I can’t recommend this for reading as a book. But if you already know your way around the Gödelian themes, you could perhaps treat this Element as an occasionally useful scrapbook to dip into, to follow up various references (indeed, some new to me). And I’ll leave it at that.

4 thoughts on “Juliette Kennedy, Gödel’s Incompleteness Theorems”

  1. I agree about the quality of the physical books (as in my comment on the Burgess one).

    I still prefer to read a paper copy, though, and I’m wondering why you suspect thy are primarily designed for online reading? (Are they even available for online reading, apart from Restall’s Proofs and Models?) (I suppose Kindle editions can be read that way, though I’d normally use a Kindle. They’re nearly as expensive as the paperbacks, though.)

      1. Thanks! It’s interesting that they were ‘conceived for a digital environment’. I wonder what that amounts to, though. Is there something about the format or content of the books that makes it seem they were primarily designed for online reading? I’ve looked at the pdf for the Restall book, and apart from having internal links, there didn’t seem to be.

        For example, are the things that aren’t positioned correctly in the diagrams in Bell’s Higher-Order Logic and Type Theory positioned correctly in the pdf? (See, for instance, the ‘(**)’ diagram at the bottom of p 6. The two circle-arrows should show $ and@ each pointing back to itself. Instead they’re positioned too far to the right.)

        In any case, there’s a serious quality-control issue with at least some of these books, so that they need st least one more proofreading pass than they were given.

        1. Philippos Papayannopoulos

          Good catch about the (**) in Bell’s book. I can confirm that it is not different in the pdf version, and that the (**) looks exactly the same in the physical and pdf version of the book.

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