Wittgenstein's May-June 1913 critique of Russell's multiple-relation theory of judgement (or MRTJ) marked a crucial turning point in the lives of two great twentieth-century thinkers. It was also a watershed moment within the history of analytic philosophy itself. Yet scholarly consensus around a satisfactory interpretation of the nature of the critique, the extent of and reasons for its impact on Russell, along with the role it played within Wittgenstein's development have remained elusive. With these facts in mind, this book aims to accomplish four interrelated goals. The first is to develop a compelling reading of Wittgenstein's May-June 1913 critique of Russell's MRTJ. The second is to defend this reading, called the 'logical interpretation' (or LI) against its most prominent competitors in the scholarly literature. Third, the book aims to situate Wittgenstein's critique of the MRTJ and Russell's reaction to it, within the broader context of each of Wittgenstein's and Russell's respective philosophical developments. Fourth and finally, the book aims to introduce students and scholars of early analytic philosophy to, and familiarize them with the historical events, textual evidence, scholarly controversies, letters, notes and diagrams, consideration of which is integral to constructing a plausible reading of Wittgenstein's objection.