Introduction

Abstract

Herbrand’s principal concern in his logical writings was to develop a unified approach to all questions of proof theory. He based this approach on his Fundamental Theorem, which is, as Bernays has remarked (1954), “the central theorem of predicate logic”. In addition to providing both information about the structure of logical proofs and a method for obtaining consistency and decidability results, this theorem also furnishes constructive insight into nonconstructive notions such as satisfiability. However, due in part to the difficulty of Herbrand’s texts and in part to surface similarities with work of Skolem and Gentzen, Herbrand’s mode of investigation is not widely understood today. In order to appreciate fully the importance of his results and their place in the history of logic, it is helpful to trace the major influences on Herbrand’s work: Whitehead and Russell’s Principia Mathematica, Löwenheim 1915 and Skolem 1920, and the articles of the Hilbert school which appeared during the 1920’s.