Russell: The Journal of Bertrand Russell Archives

Reviews 175 THE HISTORY OF RUSSELeS PYTHAGOREAN MYSTICISM STEFAN ANDERSSON Theology and Religious Studies I University of Lund 5-223 62, Lund, Sweden SANDER5S@CHASS.UTORONTO.CA Ray Monk. Russell: Mathematics: Dreams and Nightmares. (The Great Philosophers .) London: Phoenix, 1997. Paperbound. Pp. vi, 58. £2.00. CDN$4·99· R ay Monk's short book on Russell is number seven in a series of books called The Great Philosophers. Since there is neither a publisher's foreword nor an author's preface, the only suggestion concerning the content is the subtitle Mathematics: Dreams and Nightmares. For those familiar with Monk's earlier work on Wittgenstein and Russell and his understanding of the relationship between them, it will corne as no surprise that Monk has chosen this theme for his little book. His essay has two parts: 'The Pythagorean Dream" and "The Mathematician 's Nightmare". In the first part Monk describes the content, origin, and development of the Pythagorean dream up to Russell's discovery of his paradox . The second part is devoted to showing how the dream turned into a nightmare, mainly due to Wittgenstein's influence. Monk traces the origin of the dream back to an experience that Russell had at the age of eleven, when his older brother Frank gave him lessons in geometry. Russell described the experience as being "as dazzling as first love" and went on to say that from that moment until he finished Principia Mathematica , written with his former teacher Alfred North Whitehead, "mathematics was my chief interest, and my chief source of happiness." What made geometry so attractive to Russell was that it purported to provide him and everyone else with knowledge that was so certain that no reasonable man could question its truth. Certainty was the goal and mathematics the means, but the study of mathematics and the contemplation of its objects and eternal truths became an end in itself. For a period of Russell's life it was more than a dream or a source of happiness; it developed into Russell's personal religion, or "a form of mysticism" according to Monk. In several of his autobiographical writings Russell confessed that he had hoped the study of philosophy would provide some satisfaction for his religious impulses. In "Why I Took to Philosophy" (1955) he stated that: 176 Reviews For a time I found satisfaction in a doctrine derived, with modification, from Plato. According to Plato's doctrine, which I accepted only in a watered-down form, there is an unchanging timeless world of ideas of which the world presented to our senses is an imperfect copy. Mathematics, according to this doctrine, deals with the world of ideas and has in consequence an exactness and perfection which is absent from the everyday world. This kind of mathematical mysticism, which Plato derived from Pythagoras, appealed to me. (PfM, p. 22) This passage does nor really convey just how much this "mathematical mysticism ", or "Pythagorean mysticism"as Monk also calls it, once appealed to Russell. In "The Study of Mathematics" and ocher writings, as well as his letters written in the first decade of the century, we find more passionate confessions of his faith-or "personal religion" or "Pythagorean mysticism"call it what you will. The fact is that Russell's fascination with mathematics and his hope of proving that all of pure mathematics can be deduced from a small number of logical definitions and axioms-his logicism-was for a period mixed up with his religious yearnings and impulses. I have argued for chis thesis in my doctoral dissertation, In Quest ofCertainty .' Since my thesis ends with 1903, I did not discuss his attempts to solve the paradox. Nor, for the same reason, did I discuss Wittgenstein's influence on his thinking or address the question why Wittgenstein's definition of "logic" as consisting of tautologies supposedly led Russell to a linguistic interpretation of mathematics, which shattered his earlier Platonic or Pythagorean view of the nature of mathematics. At the time, I had done some research on his later development, so I had an idea about why he gave up his mathematical mysticism and when it happened. I will return to this in...