Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

First published in 1903, _Principles of Mathematics_ was Bertrand Russell’s first major work in print. It was this title which saw him begin his ascent towards eminence. In this groundbreaking and important work, Bertrand Russell argues that mathematics and logic are, in fact, identical and what is commonly called mathematics is simply later deductions from logical premises. Highly influential and engaging, this important work led to Russell’s dominance of analytical logic on western philosophy in the twentieth century.

Bertrand Russell is concerned in this book with the foundations of knowledge. He approaches his subject through a discussion of language, the relationships of truth to experience and an investigation into how knowledge of the structure of language helps our understanding of the structure of the world. This edition includes a new introduction by Thomas Baldwin, Clare College, Cambridge.

A survey such as this by one of the world's leading thinkers of his entire philosophical canon, is clearly as important as it is fascinating.

Studies the central topics of Wittgenstein's philosophy prior to and within the first parts of the Tractatus, covering such subjects as objects, substance, states of affairs, elementary propositions, pictures, and thoughts. He concludes that analysis is reduction to what is basic not in experience but in reference, and argues that the Tractatus is concerned not with problems of knowledge but with problems of sense.

Ludwig Wittgenstein was born in Vienna in 1889 and died in Cambridge in 1951. He studied engineering, first in Berlin and then in Manchester, and he soon began to ask himself philosophical questions about the foundations of mathematics. What are numbers? What sort of truth does a mathematical equation possess? What is the force of proof in pure mathematics? In order to find the answers to such questions, he went to Cambridge in 1911 to work with Russell, who had just (...) produced in collaboration with Whitehead (1861-1947) Principia Mathematica (1910-1913), a monumental treatise which bases mathematics on logic. But on what is logic based? Wittgenstein's attempt to answer this question convinced Russell that he was a genius. During the 1914-8 war he served in the Austrian army and in spare moments continued the work on the foundations of logic which he had begun in 1912. His war-time journal, Notebook s 1914-16 (1961), reveals the development of his ideas more clearly that the final version, Tractatus Logico- Philosophicus, which he published in the early 1920s. (shrink)

It is well known that Russell abandoned his multiple-relation theory of judgment, which provided the philosophical foundations for _PM_'s ramified type-theory, in response to criticisms by Wittgenstein. Their exact nature has remained obscure. An influential interpretation, put forth by Sommerville and Griffin, is that Wittgenstein showed that the theory must appeal to the very hierarchy it is intended to generate and thus collapses into circularity. I argue that this rests on a mistaken interpretation of type-theory and suggest an alternative one (...) to explain Russell's reaction. (shrink)

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

This study offers a novel integration of distinct aspects of Russell's thought.

Analytic philosophy has become the dominant philosophical tradition in the English-speaking world. This book illuminates that tradition through a historical examination of a crucial period in its formation: the rejection of Idealism by Bertrand Russell and G.E. Moore at the beginning of the twentieth century, and the subsequent development of Russell's thought in the period before the First World War.

In establishing unexpected cross-connections between physics, the theory of perception, and logic, Hyder also makes a valuable contribution to the history of ...

Russell's 1913 manuscript Theory of Knowledge was not published until 1984. He supposedly abandoned the main part of the manuscript, while publishing the first six chapters as articles in The Monist, due to Wittgenstein's criticisms of his “multiple relation” analysis of belief. There have been numerous unsuccessful and erroneous attempts to interpret the manuscript, including those of D. Pears and G. Landini. The paper explores the Russell‐Wittgenstein “controversy” and shows the radical way Russell altered his earlier versions of his analysis (...) of belief and the connections the changes had to his new, and very important, analyses of relational order, of truth as correspondence, and of propositions. Russell's analysis of relational order reveals the first recognition by a correspondence theorist of a fundamental problem the correspondence theory faces as well as a long overlooked and unappreciated application Russell made of his theory of definite descriptions. (shrink)

In his critical notice of Russell's Theory of Knowledge, R. E. Tully takes issue with my interpretation of Wittgenstein's criticism of Russell's theory of judgment. Against it he raises two objections and also sketches an alternative interpretation. On Tully's characterization, I believe that Russell was shot out of the tree by a subtle but devastating argument, while Tully believes that he was shaken out of the tree by a much broader but non-lethal attack on his conception of a proposition. The (...) metaphor is not inappropriate. I certainly believe that Wittgenstein's attack was lethal to Russell's theory of judgment and shows extraordinary marksmanship. But I do not want to deny that there was a lot of tree shaking going on at the same time—concerning, in particular, the logical constants and the concept of a proposition, both of which were topics closely related to the theory of judgment. Thus, while I maintain that Russell was shot, I do not subscribe to a single-bullet theory. (shrink)

The paper describes the evolution of russell's theory of judgment between 1910 and 1913, With especial reference to his recently published "theory of knowledge" (1913). Russell abandoned the book and with it the theory of judgment as a result of wittgenstein's criticisms. These criticisms are examined in detail and found to constitute a refutation of russell's theory. Underlying differences between wittgenstein's and russell's views on logic are broached more sketchily.

This paper offers an interpretation of Russell's multiple-relation theory of judgment which characterizes it as direct application of the 1905 theory of definite descriptions. The paper maintains that it was by regarding propositional symbols (when occurring as subordinate clauses) as disguised descriptions of complexes, that Russell generated the philosophical explanation of the hierarchy of orders and the ramified theory of types of _Principia mathematica (1910). The interpretation provides a new understanding of Russell's abandoned book _Theory of Knowledge (1913), the 'direction (...) problems' and Wittgenstein's criticisms. (shrink)

In the unpublished work Theory of Knowledge a complex is assumed to be “anything analyzable, any‐ thing which has constituents” , and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex” . The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, (...) on the role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical‐ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM. (shrink)

In the unpublished work Theory of Knowledge a complex is assumed to be “anything analyzable, any‐ thing which has constituents”, and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex”. The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, on the (...) role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical‐ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM. (shrink)

In his 1918 lectures, _The Philosophy of Logical Atomism_, Russell discusses the impossibility of drawing a diagram or "map-in-space" of the form of belief (judgment). In this paper, I argue that an examination of diagrams appended to Russell's _Theory of Knowledge_ shows him already anticipating this symbolizing difficulty in 1913 and—in the midst of attempting to adopt Wittgenstein's doctrine of propositional bipolarity—jettisoning attempts to diagram the form of belief.

Parts of the book date back to and some of the concluding remarks on ethics and the will may have been composed still earlier, when Wittgenstein admired ...

THE PHILOSOPHY which I advocate is generally regarded as a species of realism, and accused of inconsistency because of the elements in it which seem contrary to that doctrine. For my part, I do not regard the issue between realists and their opponents as a funda- mental one; I could alter my view on this issue without changing my mind as to any of the doctrines upon which I wish to lay stress. I hold that logic is what is fundamental (...) in philosophy, and that schools should be characterized rather by their logic than by their metaphysic. My own logic is atomic, and it is this aspect upon which I should wish to lay stress. Therefore I prefer to describe my philosophy as "logical atomism," rather than as "realism," whether with or without some prefixed adjective. (shrink)

This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's (...) philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)

Bertrand Russell remains one of the greatest philosophers and most complex and controversial figures of the twentieth century. Here, in this frank, humorous and decidedly charming autobiography, Russell offers readers the story of his life – introducing the people, events and influences that shaped the man he was to become. Originally published in three volumes in the late 1960s, _Autobiography_ by Bertrand Russell is a revealing recollection of a truly extraordinary life written with the vivid freshness and clarity that has (...) made Bertrand Russell’s writings so distinctively his own. (shrink)

Published in 1903, this book was the first comprehensive treatise on the logical foundations of mathematics written in English. It sets forth, as far as possible without mathematical and logical symbolism, the grounds in favour of the view that mathematics and logic are identical. It proposes simply that what is commonly called mathematics are merely later deductions from logical premises. It provided the thesis for which _Principia Mathematica_ provided the detailed proof, and introduced the work of Frege to a wider (...) audience. In addition to the new introduction by John Slater, this edition contains Russell's introduction to the 1937 edition in which he defends his position against his formalist and intuitionist critics. (shrink)

First published in 1984 as part of The Collected Papers of Bertrand Russell, Theory of Knowledge represents an important addition to our knowledge of Russell's thought. In this work Russell attempts to flesh out the sketch implicit in The Problems of Philosophy. It was conceived by Russell as his next major project after Principia Mathematica and was intended to provide the epistemological foundations for his work. Russell's subsequent difficulties in presenting his theory of knowledge, brought on by what he considered (...) to be devastating criticisms of Wittgenstein, led to both his abandonment of this work and to a major transformation in his thought. Theory of Knowledge, now available for the first time in paperback, gives us a picture of one of the great minds of the twentieth century at work. It is possible to see the unsolved problems left without disguise or evasion. This second edition has retained the full scholarly introduction. The photographs of the manuscript, appendices, and notes on textual matters have been eliminated to provide a concise and accessible guide to understanding both Russell's own thought and his relationship with Wittgenstein. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)