Once upon a time, John Corcoran and Stewart Shapiro reviewed a little book, by distinguished authors, from a distinguished press, What is Mathematical Logic edited by John N. Crossley (OUP, 1972). It’s the nightmare of getting to deserve a review like that which might rather slow a chap down as he tries to revise his own logic text …
“Incompetent performance by competent people…”. Nightmare is right. Isn’t it the job of publishers to keep books away from reviewers like that?
This line from the review: “[The mathematical mistake can be seen as the result of a pedagogical mistake, viz. using one set of primitives and giving the axioms in another.]”
made me think of one of my favorite prop. calc. exercises, from Joel Robbin’s great book.
(The last sentence of the exercise gives the point.)
Robbin’s prop calc exercise 7
I think the key to what happened is in this sentence in the review: “As indicated by several reviews in English, French and German, an expert in logic can read the book through and be left with the impression that the authors have succeeded in their aim.” For the authors were such experts themselves, and I suspect they read the book through and were left with just that impression.