Some of the rhetoric of this book is annoying. Franks is one of those philosophers who, after claiming to have taken the "naturalist turn," turn to talking as if there was a clear distinction between philosophy (retrogressive, usually foundationalist) and science (progressive, in no need of foundation): Hilbert's philosophical contribution, the claim seems to be, was to have removed questions of consistency from philosophy and transplanted them into mathematics, and this is evidence of his deep and original philosophical insight. Hilbert is praised for his indifference to questions of "foundations," and his hope — prominent at least in his polemical writings — that (finitistic) consistency proofs would justify classical mathematics against the philosophical (both men, of course, having been both mathematicians and philosophers!) criticisms of Brouwer and Weyl is correspondingly downplayed. But the rhetoric of the introductory and concluding chapters should not distract the reader from the challenging and novel discussion of the aims and fabric of proof theory in the central chapters.