This book investigates whether second-order logic can provide a robust foundation for mathematics without relying on the traditional, problematic tenets of foundationalism. Stewart Shapiro, a prominent philosopher of mathematics, examines the logical and ontological commitments required to sustain mathematical practice. He argues that second-order logic offers a more accurate reflection of mathematical reasoning than first-order alternatives, despite the inherent limitations of completeness.

Experts in the field of mathematical logic recognize this work as a significant contribution to the debate over the adequacy of first-order logic as a universal language for mathematics. Readers frequently note the technical density of the prose, which requires a strong background in formal logic to fully grasp the author's arguments.