The formal sciences, particularly mathematics, have had a profound influence on the development of linguistics. This insightful overviewlooks at techniques that were introduced in the fields of mathematics, logic, and philosophy during the twentieth century, and explores their effect on thework of various linguists. In particular, it discusses the foundations crisis that destabilised mathematics at the start of the twentieth century, the numerous related movements which sought to respond to this crisis, and how they influenced the development of syntactic theory in the 1950s. This book provides a ground-breaking and detailed reassessment of Chomsky’s early work, and concludes by discussing the resulting major consequences for current syntactic theory.