This is a pretty shameless trailer for my forthcoming book (which I confess I’m still fiddling with, since the final final version doesn’t have to with the Press for a week more).

It’s fun and illuminating to show that the First Incompleteness Theorem can be proved without any appeal to sentences that “say” that they are unprovable, or indeed without any appeal to the apparatus of Gödel numbering, Diagonal Lemmas and the like. This can be done in various ways, of course. But there is a simple argument from Kleene’s Normal Form theorem to Incompleteness, which doesn’t seem to be well known. Here’s a version extracted from the book — a version that relies on Church’s Thesis, but only to save labour and make for cuteness. Enjoy! Pre-order the book on Amazon for lots more where that came from!