“An Essay on the Foundations of Geometry”

Abstract

''An Essay on the Foundations of Geometry" Part of the new Russell bibliography which Harry Ruja and I are compiling is devoted to lengthy technical descriptions of his books. But interspersed are, I hope, more interesting accounts of what might be called the "bio-bibliographical" background to each book. The purpose of these accounts is to bring together tile various remarks which Russell himself made on the books, plus whatever else of relevance I can locate in the Archives. The account of Russell's second published book follows. An Essay on the Foundations of Geometry (Cambridge, 1897) had its origin in Russell's fellowship dissertation. After a year of indecision as to whether to write on economics or non-Euclidean geometry, he chose the latter and "settled that I would be influenced [as to his subsequent work] by the opinions of the Cambridge examiners". (See his littleknown article, ."A Turning Point", Saturday Book, 1948.) The dissertation was written at Fernhurst in the spring and summer of 1895. As Russell says in the Autobiography (Allen & Unwin, I, 125), this was "my first experience of serious original work ....when my dissertation was 'finished, I fUlly believed that I had solved all philosophical questions connected with the foundations of geometry." The dissertation was submitted in August 1895 and examined by A.N. Whitehead and James Ward. Their remarks, before Russell received word of his election to a fellowship, almost discouraged him from pursuing philosophy as a career. This is evident from a letter he wrote Alys on 9 October 1895: Thy letter cheered me after a rather depressing talk I have just had with Whitehead. He says he and Ward (who are both ultra-empiricists ) disagreed with almost every view I advocated; Ward also found my metaphysic and Psychology rather thin - like my chances, I thought when Whitehead told me. So I don't think I shall be elected tomorrow, and I suspect I am not much good at Philosophy. •.• The only thing he said that was pleasant was that certain parts, more or less as they stood, were well worth publishing. - Adieu to sweet dreams: In Portraits from Memory, Russell reports that Whitehead's wife rebuked him for criticizing Russell so harshly. But Whitehead retorted he thought it was the last chance anyone would get of finding serious fault with Russell's work (Allen and Unwin edition, p. 92-3). After its acceptance, Russell re-wrote the dissertation (apparently in 1896), and delivered the substance of it as lectures at Bryn Mawr and Johns Hopkins that autumn. He wrote to Dr. James Carey Thomas (an uncle 'of Alys's and connected with Johns Hopkins) on 3 July 1896: ••• My lectures would be an expansion of a dissertation which I submitted when I was elected a fellow of Trinity College, Cambridge ; since my election, I have continued to work at the same subject, and I hope that the Cambridge University Press will publish a book by me on the subject, during the course of the next year. Russell is found writing in much the same way to Carey Thomas, President of Bryn Mawr. His agreement with the Cambridge University Press is dated 28 September 1896. 750 copies of the ,book were printed and published in June 1897. Russell says that the book, when published, was "highly praised, far more highly in fact than it deserved. Since that time, academic reviewers have generally said of each successive book of mine that it showed a falling-ofP' (Autobiography, I, 130). In later years Russell considered The Foundations much too Kantian and "somewhat foolish": "the. geometry in 'EinsteinI s General Theory of Relativity is such as I had declared to be impossible•.•Apa~t from d~3 tails, I do not think that there is anything valid in this early book" (MY Philosophical Development, p. 39-40). For the French translation, published in 1901, Russell added a new preface, made a "Rreat number" of corrections and additions to the text - some of quite considerable importance, he remarks - and appended notes on mathematical concepts. Louis Couturat also revised ahd annotated the text, and appended definitions of some philosophical terms. The translator , Albert Cadenat, often solicited Russell's advice...