Abstract

Bertrand Russell's Principia Mathematica has played a crucial role in the development of modem logic and philosophy. Notwithstanding its considerable influence, Principia's contents are not well known and, in important respects, not well understood today. Although several commentaries about Principia have appeared since its publication, most of these mischaracterise several of its gross structural features--for instance, those by Copi, Kleene, Kneale, and Ramsey--and even some of the better commentaries remain unclear about its details--for instance, those by Chihara, Hylton, and Quine. ;This dissertation examines Principia Mathematica in detail. The examination is carried out in light of four general aims. The first is to explain the nature of the logical theory that Russell endeavoured to put forward in Principia. The second is to examine how Russell put Principia's logical theory to work to serve his various ends. The third is to show how this local theory's general structural features and several of its details relate to the wealth of ideas that Russell seriously entertained and pursued in the period in which he was working on Principia. Finally, the fourth aim is to compare Russell's conception of his local theory with contemporary conceptions of logic. ;The dissertation is divided into five chapters. Chapter 1 discusses some of the ends that Russell set for himself in his 1903 Principles--ends which he intended the logical theory of Principia to accomplish. The next two chapters look at the antecedents to this logical theory: Chapter 2 examines the local theory of Principles and Chapter 3 examines Russell's celebrated vicious-circle principle. The last two chapters describe the local theory proper of Principia: Chapter 4 explains the theory's propositional fragment and Chapter 5 explains its quantificational fragment. This last chapter also details the theory's type-theoretic features