In 1911, Bertrand Russell began a historically formative interchange about the nature of logic and cognition with his student, Ludwig Wittgenstein. In 1913, Russell set to work on a manuscript, the "Theory of Knowledge", designed to move from the analysis of perception to judgement and on to knowledge of the world. After Wittgenstein interrupted Russell's daily writing with a series of objections to his doctrine of judgement and conception of logic, Russell abandoned his project in despair, leaving it unfinished. His subsequent work can be understood largely as an attempt to assimilate and respond to Wittgenstein's challenge in 1913. "Russell and Wittgenstein on the Nature of Judgement" is the first book-length treatment of Russell's decisive 1913 exchanges with Wittgenstein. Rosalind Carey incorporates little-known notes and diagrams into a new analysis of the problems Russell was facing. She also evaluates the numerous interpretations of Russell's positions and Wittgenstein's objections to them. The result is a new perspective on both these great thinkers, at a crucial point in the development of twentieth-century philosophy.