This fourth and final volume of the monumental commentary on Wittgenstein's Philosophical Investigations covers pp. 428-693 of the book. Like the previous volumes, it consists of philosophical essays and exegesis. The nine essays cover all the major themes of this concluding part of Wittgenstein's masterpiece: intentionality, inductive reasoning, the arbitrariness of grammar and the bounds of sense, negation, methodology in philosophical psychology, memory and recognition, willing and the nature of voluntary action, intending, and the mythology of meaning something. Wittgenstein's writings on some of these themes have been relatively neglected, and the analytical essays on the topics of intentionality, the arbitrariness of grammar, and the will shed fresh light upon his characteristically original contributions to these subjects, which are highly relevant to current debates. The exegesis clarifies and evaluates Wittgenstein's arguments, drawing extensively on all the unpublished papers, examining the evolution of his ideas in manuscript sources and definitively settling many controversies about the interpretation of the published text.This commentary, like its predecessors, is indispensable for the study of Wittgenstein and is essential reading for students of philosophy of mind and philosophy of language.The completion of the Commentary will be followed by a historical monograph entitled Wittgenstein's Place in Twentieth Century Analytic Philosophy, which will give an overview of Wittgenstein's achievement, locate his work within the mainstream of analytic philosophy and examine his influence upon the development of Cambridge analysis in the interwar years, upon the Vienna Circle and upon postwar Oxford analytic philosophy.