This volume shows Russell in transition from a neo-Kantian and neo-Hegelian philosopher to an analytic philosopher of the first rank. During this period, his research centred on writing The Principles of Mathematics where he drew together previously unpublished drafts. These shed light on Russell's paradox. This material aims to alter previous accounts of how he discovered his paradox and the related paradox of the largest cardinal. The volume also includes a previously unpublished draft of an early attempt to solve his paradox, as well as the earliest known version of his generalized...

The Axiom of Choice is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma). This treatment is the only full-length history of the axiom in English, and is much more complete than the two other books on the subject, one in French and the other in Russian. This book covers the Axiom's prehistory of implicit uses in the 19th century, its explicit formulation by Zermelo in 1904, the firestorm of controversy that it...