This book has many virtues. It is concentrated on fundamental questions in the philosophy of mathematics, which it explores with an open mind – or even two open minds; it is richly informed and informative in its clear exposition of the details of nominalistic reconstruction programs, indeed the whole extant gamut of them, some themselves usefully reconstructed; it concludes with a novel insight into the unsuspected value of these programs (to be explained below); and, of special immediate relevance, it is remarkably balanced in its argumentation and self-contained, even to the point of containing its own review! Not verbatim, of course, but implicitly, as a scattered whole, merely awaiting a judicious selection and assembly, with occasional textually inspired critical commentary. Here follows an attempt at such.