The second paper in the collection is a seven-page ramble by Georg Kreisel, followed by twenty pages of mostly opaque endnotes. This reads in many places like a cruel parody of the later Kreisel’s oracular/allusive style. I lost patience very quickly, and got almost nothing from this. What *were* the editors doing, printing this paper as it is? (certainly no kindness to the author).

Something that struck me though, from the footnotes. Kreisel “saw a good deal of Bernays, who liked to remember Hilbert …. According to Bernays … Hilbert was asked (before his stroke) if his claims for the ideal of consistency should be taken literally. In his (then) usual style, he laughed and quipped that the claims served only to attract the attention of mathematicians to the potential of proof theory” (pp. 42–43). And Kreisel goes on to say something about Hilbert wanting use consistency proofs to bypass “then popular (dramatized) foundational problems and get on with the job of doing mathematics”. Which chimes with Curtis Franks’s ‘naturalistic’ reading of Hilbert, which I discussed here.

The book’s next contribution couldn’t be more of a contrast, at least in terms of crisp clarity. Ivor Grattan-Guinness is his usual lucid and historically learned self when writing quite briefly about ‘The reception of Gödel’s 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s’. But in a different way I also got rather little out this paper. There are some interesting little anecdotes (e.g. Saunders Mac Lane studied under Bernays in Hilbert’s Göttingen in 1931 to 1933 — but writes that that he was not made aware of Gödel’s result). But the general theme that logicians got to know about incompleteness early (with some surprising little delays), and the word spread among the wider mathematical community much more slowly could hardly be said to be excitingly unexpected. Grattan-Guinness has J. R. Newman as a hero populariser (and indeed, I think I first heard of Gödel from his wonderful four-volume collection *The World of Mathematics*) — and Bourbaki is something of a anti-hero for not taking logic seriously. But, as they say, what’s new?