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This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its ...

Russell's involuted path in the development of his theory of logical types from 1903 to 1910-13 is examined and explained in terms of the development in his early philosophy of the notion of a logical subject vis-a-vis the problem of the one and many; i.e., the problem for russell, first, of a class-as-one as a logical subject as opposed to a class as many, and, secondly, of a propositional function as a single and separate logical subject as opposed to existing (...) only in the many propositions that are its values. (shrink)

All these specialist aspects of one life are different facets of the intellectual diamond which scintillates in the huge quarry of The Bertrand Russell Archives at McMaster University, Hamilton, Ontario. This is the quintessential man, the bundle of contradictions passionately dedicated to intellect, at times carrying the rational argument to irrational extremes; the natural-born emotional adventurer forever hampered by orphaned youth and too-early marriage. This Russell in the round is greater than the sum of his constituent parts, a man of (...) epic proportions, struggling through a lifetime beset with frustration and near-disaster; in youth the constitutional sceptic, in old age the sometimes splendid figure with "courage never to submit or yield.". (shrink)

Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...) philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gode1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Godel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.". (shrink)

This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.

Among the papers left by Bertrand Russell (1872?1970) and now held at the Russell Archives at McMaster University, is a large quantity of material on mathematical logic and the foundations of mathematics. This paper is a provisional survey of their extent and content. Some indications are given of their historical significance, and a discussion is added to the possible modes of their publication in the edition of Russell's Collected papers, currently in progress.

This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a version or modification of the substitutional (...) theory. New motivations for Russell's 1908 axiom of infinity and axiom of reducibility are revealed. (shrink)

This paper describes the materials in the Russell Archives relevant to Russell's work on logic and the foundations of mathematics, and suggests the kinds of information that may and may not be drawn about the historical development of his ideas. By way of illustration, a couple of episodes are described. The first concerns a logical system closely related to his theory of denoting, which preceeds the system used in Principia mathematics, while the second describes a delay in publishing the second (...) volume of that work due to the discovery by Whitehead of a conceptual error. (shrink)

According to the received view, Russell rediscovered about 1900 the logical definition of cardinal number given by Frege in 1884. In the same way, we are told, he stated and developed independently the idea of logicism, using the principle of abstraction as the philosophical ground. Furthermore, the role commonly ascribed in this to Peano was only to invent an appropriate notation to be used as mere instrument. In this paper I hold that the study of Russell's unpublished manuscripts and Peano's (...) (and disciples) writings (as part of a larger investigation only pointed out here) shows, on the contrary, that Russell obtained the method to transform definitions by abstraction into nominal definitions and the general logicist idea from Peano (and his school). The only original insight from Russell, the principle of abstraction, partially derived from Moore's early philosophy, was finally abandoned because it was not of practical use. (shrink)

In this article I propose a new explanation of the relationship between Russell and ther first Wittgenstein. There are five main novelties in my interpretation; the use of all relevant unpublished manuscripts of Russell; the discovery of the first apparition of the “multiple theory of judgment” in a purely logical and unpublished context; the role of the Bradleian objection against relations in the evolution of the nation of form in both Russell and Wittgenstein; a general point of view to obtain (...) a common explanation of all the criticisms of Wittgenstein against Russell and of the abandonment to Theory of Knowledge; and the first account of the contribution of Whitehead to the progressive Russellian evolution from atomism to holism. (shrink)