An account is given of the emergence of the concept of work as a basic component of mechanics. It was largely an achievement of engineer savants in France during the Bourbon Restoration , with Navier, Coriolis and Poncelet playing the major roles. Some aspects of the eighteenth-century prehistory are described, and also concurrent developments in French engineering. The principal problem areas were friction, hydraulics, machine performance and ergonomics, and especially in the last context the developments became involved with social and (...) even philosophical movements in the 1820s. Education played an important role throughout; several of the principal sources are textbooks. (shrink)

SummaryIn June 1913 the 18-year-old Norbert Wiener presented to Harvard University a doctoral thesis comparing the logical systems of Schröder and Russell, with special reference to their treatment of relations. Shortly afterwards he visited Russell in Cambridge (England) and showed him a copy of the thesis. Russell wrote out some comments, to which Wiener replied.None of these documents has been published. In this paper I summarise the contents of Wiener's thesis, and describe and quote from the subsequent discussion with Russell. (...) I preface the account with some remarks on the personal relationship of Wiener and Russell, and conclude it with the description of the location of the various documents cited. (shrink)

Although the existence of correspondence between George Boole (1815?1864) and William Stanley Jevons (1835?1882) has been known for a long time and part was even published in 1913, it has never been fully noted; in particular, it is not in the recent edition of Jevons's letters and papers. The texts are transcribed here, with indication of their significance. Jevons proposed certain quite radical changes to Boole's system, which Boole did not accept; nevertheless, they were to become well established.

The great influence of Georg Cantor's theory of sets and transfinite arithmetic has led to a considerable interest in his life. It is well known that he had a remarkable and unusual personality, and that he suffered from attacks of mental illness; but the ‘popular’ account of his life is richer in falsehood and distortion than in factual content. This paper attempts to correct these misrepresentations by drawing on a wide variety of manuscript sources concerning Cantor's life and career, including (...) the texts of some important documents. An appendix describes the most important collection of missing manuscripts, whose location would help further the preparation of a biographical study of Cantor. (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)

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (...) (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic", which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written. (shrink)

Graham Priest argued that all the paradoxes of set theory and logic fall under one schema; and hence they should be solved by one kind of solution. This reply addresses both claims, and counters that in fact at least one paradox escapes the schema, and also some apparently "safe" theorems fall within it; and even for the range of paradoxes so captured by the schema, the assumption of a common solution is not obvious; each paradox surely depends upon the theory (...) and context in which it arises. Details of Priest's proposed solution are also sought. (shrink)

In this paper I consider three mathematicians who allowed some role for menial processes in the foundations of their logical or mathematical theories. Boole regarded his Boolean algebra as a theory of mental acts; Cantor permitted processes of abstraction to play a role in his set theory; Brouwer took perception in time as a cornerstone of his intuitionist mathematics. Three appendices consider related topics.

The ArgumentThis paper deals with the achievements of those French mathematicians active in the period 1800–1830 who oriented their work specifically around the needs of engineering and technology. In addition to a review of their achievements, the principal organizations and institutions are noted, as is their importance as sources of employment and influence.The argument is centered on the word ‘neglected“ in the title. A case is made that a mass of work was produced which made considerable impact at the time (...) but has been overlooked or even completely ignored by historians since. The paper begins with a general discussion of the notion of context, both for the historical figures and for their supposed historians, and several examples of historical distortion are given.Regarding France itself, we see a professional and research profile rather different from that in other countries. The question of national differences in the organization and prosecution of science is thereby sharply exposed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BROADCAST REVIEW OF HISTORY OF WESTERN PHILOSOPHY[I] K. R. POPPER Translated by I. GRATTAN-GUINNESS B ertrand Russell has written a new book.[2] It is a great work, great in its ideas, great in its inspiration and great in its significance. The title is: A History ofwestern Philosophy, in German, Geschichte der Abendlaendischen Philosophie. The book can well be called unique. In any case, it is the first of its (...) kind. There are many histories of philosophy, multi-volumed and single-volumed, good and bad. But up to now there has not been one written by a really great and original thinker. Most were written by well-trained scholars, but there is a great difference between a scholarly professor of philosophy who writes the history of philosophy, and a man like Russell who is himself a maker of the history of philosophy. Perhaps this explains in part the uniqueness of this book. It is a book that is written with clarity and at the same time with a cheerful ease; a book that ventures, and that can venture, to handle the history of philosophy with humour and with grace. What is special and great in Russell's book? The table of contents is not essentially different from other histories of philosophy. Russell himself describes the special purpose upon which he has settled as follows: he wants to understand each philosopher from his social context, and to explain the philosopher's special philosophy (as far as [' Broadcast over the Austrian Broadcasting Service, 19 Januaty 1947. For the German original, see pp. 11-13. The translation has been checked by Sir Karl Popper.] [2 History of W(stern Philosophy, and Its Connection with Political and Social Circumstancesfrom the Earliest Times to the Present Day (London: George Allen & Unwin Ltd., 1946). Pp. 916. £1.0.0.] russell: the Journal of the Bertrand Russell Archives McMaster University Libraty Press n.s. 12 (summer 1992): '9-2'. 1SSN 0036-01631 20 K. R. POPPER possible) through its social circumstances and the political institutions andproblems ofhis time. But in my view the aim IS hardly the special thing in Russell's book. For nowadays this method can hardly be claimed to be original any more. It is true that Russell is the first to extend this socio-historical method to the entire history of philosophy; and that this allows him to throw new light on many problems-in particular, on problems and forms of philosophy of the early middle ages, for example Augustine and Boethius. But despite the attraction of these problems, I do not believe that the greatness of Russell's book lies in its socio-historical method. What makes the book great is the man who has written it. The book is the man. By that I do not want to say that the book is less objective than other histories of philosophy. On the contrary, other books seek earnestly to be objective, but they never achieve it. What they achieve is only that they seem to be objective, and with that to give a &Ise impression to the reader. Russell does not attempt to be objective. He permits himself to state his opinion simply and openly, and he makes it quite clear that this is his personal opinion-his wellconsidered opinion-but not more; certainly not the judgment ofhistory. In my eyes, Bertrand Russell is without doubt the only man in our time of whom one can say that he is a great philosopher-a philosopher who can be named in the one breath with men like Descartes, John Locke, David Hume, or Immanuel Kant. He is the man whom we thank that philosophy has not entirely lapsed into one of the intolerable fashions of our time, and into charlatanry and wind-baggery. The expressions "charlatanry" and "windbaggery" were deployed by Schopenhauer, who saw these things and fought against them, as did Kant. Until Fichte and Hegel ruined it, philosophy was argumentation. Arguments counted-otherwise nothing. Since Fichte and Hegel philosophy has moved towards spell-weaving. It has given up instructing us, and instead seeks to beguile us, as Schopenhauer said. The trendy philosophers, who beguile us instead of instructing us, found an... (shrink)

This paper is concerned with the influence that the set theory of Georg Cantor bore upon the mathematical logic of Bertrand Russell. In some respects the influence is positive, and stems directly from Cantor's writings or through intermediary figures such as Peano; but in various ways negative influence is evident, for Russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, six sections compare and contrast their views on matters of common interest; irrational (...) numbers, infinitesimals, cardinal and ordinal numbers, the axiom of infinity, the paradoxes, and the axioms of choice. Two further sections compare the two men over more general questions: the role of logic and the philosophy of mathematics. In a final section I draw some conclusions. (shrink)

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.

The Companion Encyclopedia is the first comprehensive work to cover all the principal lines and themes of the history and philosophy of mathematics from ancient times up to the twentieth century. In 176 articles contributed by 160 authors of 18 nationalities, the work describes and analyzes the variety of theories, proofs, techniques, and cultural and practical applications of mathematics. The work's aim is to recover our mathematical heritage and show the importance of mathematics today by treating its interactions with the (...) related disciplines of physics, astronomy, engineering and philosophy. It also covers the history of higher education in mathematics and the growth of institutions and organizations connected with the development of the subject. Part 1 deals with mathematics in various ancient and non-Western cultures from antiquity up to medieval and Renaissance times. Part 2 treats developments in all the main areas of mathematics during the medieval and Renaissance periods up to and including the early 17th century. Parts 3-10 are divided into the main branches into which mathematics developed from the early 17th century onwards: calculus and mathematical analysis, logic and foundations, algebras, geometries, mechanics, mathematical physics and engineering, and probability and statistics. Parts 11-13 review the history of mathematics from an international perspective. The teaching of mathematics in higher education is examined in various countries, and mathematics in culture, art and society is covered. The Companion Encyclopedia features annotated bibliographies of both classic and contemporary sources; black and white illustrations, line figures and equations; biographies of major mathematicians and historians and philosophers of mathematics; a chronological table of main events in the developments of mathematics; and a fully integrated index of people, events and topics. (shrink)

Introduction Contrary to a widespread assumption the modern history of modal logic did not start with C. I. Lewis’ Survey of Symbolic Logic [Lewis 1918]. His eminent work was preceded by some 20 years by H. MacColl’s fifth article on ‘The Calculus of Equivalent Statements’. This article was read at the London Mathematical Society on 12 November 1896. Some months later it was published in the Society’s Proceedings [MacColl 1896-1897]. During the following years MacColl presented his logic prim...

Introduction Contrary to a widespread assumption the modern history of modal logic did not start with C. I. Lewis’ Survey of Symbolic Logic [Lewis 1918]. His eminent work was preceded by some 20 years by H. MacColl’s fifth article on ‘The Calculus of Equivalent Statements’. This article was read at the London Mathematical Society on 12 November 1896. Some months later it was published in the Society’s Proceedings [MacColl 1896-1897]. During the following years MacColl presented his logic prim...

The Scottish logician Hugh MacColl is well known for his innovative contributions to modal and nonclassical logics. However, until now little biographical information has been available about his academic and cultural background, his personal and professional situation, and his position in the scientific community of the Victorian era. The present article reports on a number of recent findings.

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in their Principia mathematica (1910-1913).? This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of (...) Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI. Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials. Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since. (shrink)

Dans la seconde moitié des années 1900, Bertrand Russell et Hugh MacColl échangèrent sans s’entendre sur les questions de l’implication et de l’existence, dans le cadre d’un débat plus général sur la nature de la logique. Il est tentant de voir dans cet échange une opposition entre le moniste logique Russell et le pluraliste MacColl. Dans cet article, j’affirme que cette interprétation est inexacte, et que les deux hommes étaient tous deux monistes, bien qu’ayant des allégeances différentes. La transition du (...) monisme au pluralisme ne s’effectue en réalité qu’à partir du début des années 1910, peu après la mort de MacColl en 1909. Les premiers signes de cette transition sont à trouver particulièrement chez le philosophe américain C. I. Lewis, le mathématicien néerlandais L. E. J. Brouwer, et le logicien polonais Jan Łukasiewicz. Ces auteurs sont des exemples de l’avènement graduel de la métalogique. (shrink)

Dans la seconde moitié des années 1900, Bertrand Russell et Hugh MacColl échangèrent sans s’entendre sur les questions de l’implication et de l’existence, dans le cadre d’un débat plus général sur la nature de la logique. Il est tentant de voir dans cet échange une opposition entre le moniste logique Russell et le pluraliste MacColl. Dans cet article, j’affirme que cette interprétation est inexacte, et que les deux hommes étaient tous deux monistes, bien qu’ayant des allégeances différentes. La transition du (...) monisme au pluralisme ne s’effectue en réalité qu’à partir du début des années 1910, peu après la mort de MacColl en 1909. Les premiers signes de cette transition sont à trouver particulièrement chez le philosophe américain C. I. Lewis, le mathématicien néerlandais L. E. J. Brouwer, et le logicien polonais Jan Łukasiewicz. Ces auteurs sont des exemples de l’avènement graduel de la métalogique. (shrink)

Symbolic logics tend to be too mathematical for the philosophers and too philosophical for the mathematicians; and their history is too historical for most mathematicians, philosophers and logicians. This paper reflects upon these professional demarcations as they have developed during the century.

In lieu of an abstract, here is a brief excerpt of the content:RUSSELL AND G. H. HARDY: A STUDY OF THEIR RELATIONSHIP I. GRATTAN-GUINNESS Faculty of Science, Engineering and Mathematics Middlesex Polytechnic Enfield, Middlesex EN3 45F, England I. INTRODUCTION Prom time to time the name of Hardy turns up in Russell's career: a common interest in set theory and the philosophy of mathematics, similar political and religious sentiments, and certain matters of mutual concern arising at Trinity College Cambridge and in (...) the university in general. However, there is no connected account of their contacts. The purpose of this article is to fill a gap in the literature on both men. After enduring private instruction at home, Bertrand Russell gained a minor scholarship in mathematics at Trinity College in 1890; he took Part I of the Mathematical Tripos until 1893 and then Part II of the Moral Sciences Tripos in the following year. In 1895 he gained a Prize Fellowship, which he held until 1901; in 19IO.he was awarded a college lectureship which he lost six years later under circumstances noted in section IV below. Much of the intervening time was spent in Oxford or London; however, he spent part of each year in Cambridge.1 The later years are brieHy recorded in section IV. Born into an intellectual family ofmodest means in 1877 (five years younger than Russell, therefore), Godfrey Harold Hardy won a scholarship to Winchester College and then went to Trinity College in I Standard biographical information on Russell is easily available; see, for example, R. W. Clark, The Life ofBertrand Russel~ specific phases and events are dealt with in succeeding footnotes. The Autobiography ofBertrand Russell is of lower quality than one might imagine; for example, Hardy is not mentioned at all! rus.ell: the Journal of the Bertrand Russell Archives McMasrer Unive~ity Library Press noS. 11 (wimer 1991-92): 165-79 ISSN 0036-01631 166 I. GRATTAN-GUINNESS 1896, just after Russell had gained his fellowship. He was elected to the Apostles (the "Society") in 1898, the year after Russell "took wings" after five years' active membership; he seems to have been less active than Russell as a speaker during his own three years there.2 At some stage he also joined the Cambridge University Moral Sciences Club, which Russell had joined in. 1891; a surprising contribution will be described in section IV.3 Graduating as fourth wrangler in Part I of the Mathematical Tripos in 1898 and gaining a high place in Part II in 1900, Hardy received at once a Prize Fellowship (like Russell). Upon its termination six years later, he obtained a colleg~ lectureship, which he held until 1919. He was elected a Fellow of the Royal Society of London in 1910 (two years after Russell),4 and in the following year he began his life-long collaboration with his younger colleague ]. E. Littlewood (1885-1977), also a Trinity College graduate and then Fellow, and also a friend of Russell.5 The next stages of Hardy's career will be described in section IV: his personality is assessed in a concluding section v. 1 On Russell'~ and Hardy's roles in the Apostles, see passim in P. Levy, Moore: G. E Moore and the Cambridge Apostles (London: Weidenfeld and Nicolson, 1979). 3 The chief obituary of Hardy is by E. C. Titchmarsh, published in slightly different forms in Obituary Notices ofthe Royal Society ofLondon, 6 (1949); 447-61, and Journal ofthe London Mathematical Society, 25 (1950): 81-101 (followed by more technical surveys of his mathematics by Titchmarsh and eight other authors on pp. 102-38). The first version is reprinted with a few changes in Hardy's Collected Papers, 7 vols. (Oxford: Clarendon P., 1966-79), I: 1-12. No major study has been written on him since. 4 Hardy was n~minated for a Royal Sociery fellowship in 1907 by A. R. Forsyth, seconded by J. W L. Glaisher, and supported "on personal knowledge" by W Burnside, E. W Hobson, P. A. MacMahon, A. N. Whitehead, A. E. H. Love, E. B. Elliott and T.]. d'A. Bromwich; the proposal was "suspended" (put up for voring) in 1908, 1909 and 1910 (Royal Sociery Cettificates, 12: foJ. 311). Although Russell was... (shrink)

Este artículo presenta un alnplio panorama histórico de las conexiones existentes entre ramas de las matematícas y tipos de lógica durante el periodo 1800-1914. Se observan dos corrientes principales,bastante diferentes entre sí: la lógica algebraica, que hunde sus raíces en la logique yen las algebras de la época revolucionaria francesa y culmina, a través de Boole y De Morgan, en los sistemas de Peirce y de Schröder; y la lógica matematíca, que tiene una fuente de inspiraeión en el analisis matemático (...) de Cauchy y de Weierstrass y culmina, a través de las inieiativas de Peano y de la teoria de conjuntos deCantor, en la obra de Russell. Se extraen algunas conclusiones generales, con referencias relativas a la situaeión posterior a 1914.This article contains a broad historical survey of the connections made between branches of mathematics and types of logic during the period 1800-1914. Two principal streams are noted, rather different from each other: algebraic logic, rooted in French Revolutionary logique and algebras and culminating, via Boole and De Morgan, in the systems of Peirce and Schröder; and mathematical logic, inspired by the mathematical analysis of Cauchy and Weierstrass and culminating, via the initiatives of Peano and the set theory of Cantor, in the work of Russell. Some general conclusions are drawn, with examples given of the state of affairs after 1914. (shrink)

Post's Nachlass has recently been made available to the public in an archive in the U.S.A. After a short summary of his life and career, this article indicates the character and content of the manuscripts, and their significance is assessed. Two short passages are transcribed; and. as a separate item, a paper of the 1930s on the paradoxes is reproduced.