This volume of Bertrand Russell's Collected Papers finds Russell focused on writing Principia Mathematica during 1905–08. Eight previously unpublished papers shed light on his different versions of a substitutional theory of logic, with its elimination of classes and relations, during 1905-06. A recurring issue for him was whether a type hierarchy had to be part of a substitutional theory. In mid-1907 he began writing up the final version of Principia, now using a ramified theory of types, and eleven unpublished drafts from 1907-08 deal with this. Numerous letters show his thoughts on the process. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of Principia went to the printer.

A long tradition, going back to Aristotle, conceives of logic in terms of necessity and possibility: a deductive argument is correct if it is not possible for the conclusion to be false when the premises are true. A relatively unknown feature of the analytic tradition in philosophy is that, at its very inception, this venerable conception of the relation between logic and necessity and possibility - the concepts of modality - was put into question. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, held that these concepts are empty: there are no genuine distinctions among the necessary, the possible, and the actual. In this book, the first of two volumes, Sanford Shieh investigates the grounds of this position and its consequences for Frege's and Russell's conceptions of logic. The grounds lie in doctrines on truth, thought, and knowledge, as well as on the relation between mind and reality, that are central to the philosophies of Frege and Russell, and are of enduring philosophical interest. The upshot of this opposition to modality is that logic is fundamental, and, to be coherent, modal concepts would have to be reconstructed in logical terms. This rejection of modality in early analytic philosophy remains of contemporary significance, though the coherence of modal concepts is rarely questioned nowadays because it is generally assumed that suspicion of modality derives from logical positivism, which has not survived philosophical scrutiny. The anti-modal arguments of Frege and Russell, however, have nothing to do with positivism and remain a challenge to the contemporary acceptance of modal notions.

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

A founder of modern analytic philosophy and one of the most important logicians of the twentieth century, Bertrand Russell has influenced generations of philosophers. The Bloomsbury Companion to Bertrand Russell explores this influence in detail and responds to renewed interest in Russell's philosophical approach, presenting the best guide to research in Russell studies today. Bringing new insights into Russell's relationship with his contemporaries, a team of experts explore his life-long battles with important philosophical issues. They consider how he influenced thinkers and schools of thought, from Schröder, Frege and Meinong to Wittgenstein and the Vienna Circle, while also covering his impact on individual issues in epistemology, logic, metaphysics, philosophy of mind, philosophy of language, and political philosophy. Importantly this companion discusses often overlooked topics. Focusing on Russell's later views, including his moral philosophy and his politics, reveals that Russell did make significant contributions to ethics - both theoretical and practical - in the course of his career. Through a combination of enlightening historical background and sustained focus on Russell's impact on contemporary areas of philosophy, The Bloomsbury Companion to Bertrand Russell demonstrates why Russell continues to influence philosophers of language, mathematics, epistemology and metaphysics.

The Collected Papers of Bertrand Russell, Volume 26 covers a period of transition in Russell's political life between his orthodox and sometimes pugnacious defence of the West in the early post-war, and the dissenting advocacy of nuclear disarmament and détente that started in earnest in the mid-1950s. While some of the assembled writings echo harsh prior criticism of Soviet expansionism and dictatorship, others register growing qualms about the recklessness of American foreign policy and the baneful effects on civil liberties of anti-communist hysteria inside the United States. Whether continuing to push for western rearmament, or highlighting in a more placatory vein the folly of the Cold War's divisions and rival fanaticisms, Russell's paramount objective was avoiding a war that threatened global catastrophe. Suspended between fear and hope, he expounded his evolving political concerns–and much else besides, including autobiographical reflections and typically common-sense guidance for living well–in a constant flow of newspaper and magazine articles, letters to editors, radio broadcasts and discussions and, of special note, a Nobel Prize acceptance speech. Russell also completed two lecture tours of the United States (the last of many), as well as a landmark such visit to Australia. All three of these journeys, and the textual record they left, are examined in depth using manuscript material and unpublished correspondence from the Bertrand Russell Archives at McMaster University, which is mined extensively throughout the volume.

Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

The concepts of particular and universal have become so familiar that their significance has become difficult to discern, like coins that have been passed back and forth too many times, worn smooth so their values can no longer be read. On the Genealogy of Universals seeks to overcome our sense of over-familiarity with these concepts by providing a case study of their evolution during the late 19th century and early 20th century, a study that shows how the history of these concepts is bound up with the origins and development of analytic philosophy itself. Understanding how these concepts were taken up, transfigured and given up by the early analytic philosophers, enables us to recover and reanimate the debate amongst them that otherwise remains Delphic - to interpret some of the early, originating texts of analytic philosophy that have hitherto baffled commentators, including Moore's early papers, to appreciate afresh the neglected contributions of philosophical figures that historians of analytic philosophy have mostly since forgot, including Stout and Whitehead, and to shed new light upon the relationships of Moore to Russell and Russell to Wittgenstein.

Bertrand Russell and the Nature of Propositions offers the first book-length defence of the Multiple Relation Theory of Judgement (MRTJ). Although the theory was much maligned by Wittgenstein and ultimately rejected by Russell himself, Lebens shows that it provides a rich and insightful way to understand the nature of propositional content. In Part I, Lebens charts the trajectory of Russell’s thought before he adopted the MRTJ. Part II reviews the historical story of the theory: What led Russell to deny the existence of propositions altogether? Why did the theory keep evolving throughout its short life? What role did G. F. Stout play in the evolution of the theory? What was Wittgenstein’s concern with the theory, and, if we can’t know what his concern was exactly, then what are the best contending hypotheses? And why did Russell give the theory up? In Part III, Lebens makes the case that Russell’s concerns with the theory weren’t worth its rejection. Moreover, he argues that the MRTJ does most of what we could want from an account of propositions at little philosophical cost. This book bridges the history of early analytic philosophy with work in contemporary philosophy of language. It advances a bold reading of the theory of descriptions and offers a new understanding of the role of Stout and the representation concern in the evolution of the MRTJ. It also makes a decisive contribution to philosophy of language by demonstrating the viability of a no-proposition theory of propositions.