Probably no group of intellectuals has had a greater impact on American politics over the last four decades than the neoconservatives. The Rolling Stones even sang a song about them. Yet who or what exactly is a neoconservative? Over the years the meaning of the word has changed. Initially it referred to a coterie of liberals and leftists, absorbed in domestic policy issues, who raised questions about the efficacy of Lyndon Johnson’s Great Society programs in the mid-1960s. Today, neoconservatives seem restricted for the most part to the Republican Party and are advocates of a muscular foreign policy. Irving Kristol, who once described himself as a liberal “mugged by reality,” was one kind of neoconservative. His son, William, a lifelong Republican, is an entirely different kind.