In The Principles of Mathematics, Bertrand Russell set forth his logicist thesis that the concepts of non-applied mathematics are those of pure logic. In this revisionist interpretation. Gregory Landini explores an important central thread that unifies Russell's thoughts on logic in the two works. The heart of Landini's book is a careful presentation and exploration of Russell's largely unpublished "substitutional" theory of propositions. Explores a central thread unifying Russell's thoughts on logic in two works considered at odds with each other: "Principles of Mathematics" and "Principia Mathematica". The thread states that logic is an absolutely general science and any calculus for it must embrace unrestricted variables.