Jourdain, Russell and the Axiom of Choice: A New Document

Abstract

June 25, 2012 (9:21 pm) E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1 060 red.wpd 1 Jourdain’s principal historical writings are gathered together in Selected Essays on the History of Set Theory and Logics (1906–1918), ed. I. Grattan-Guinness (Bologna: clueb, 1991) and his introduction to G. Cantor, Contributions to the Founding of the Theory of TransWnite Numbers, trans. and ed. Jourdain (La Salle, Ill.: Open Court, 1915; repr. New York: Dover, 1955). 2 I. Grattan-Guinness, Dear Russellz—zDear Jourdain: a Commentary on Russelly’s Logic, Based on His Correspondence with Philip Jourdain (London: Duckworth; New York: Columbia U. P., 1977); hereafter “RJy”. russell: the Journal of Bertrand Russell Studies n.s. 32 (summer 2012): 69–74 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 ocuments JOURDAIN, RUSSELL AND THE AXIOM OF CHOICE: A NEW DOCUMENT I. Grattan-Guinness Middlesex U. Business School Hendon, London nw4 4bt, uk Centre for Philosophy of Natural and Social Science, l.s.e. London wc2a 2ae, uk ivor2@mdx.ac.uk i.wcareer P hilip Edward Bertrand Jourdain (1879–1919) went up to Trinity College Cambridge in 1899 with a scholarship in mathematics. Two years later he attended a special College course in mathematical logic oTered by Bertrand Russell, the Wrst of its kind ever taught in a British university. This contact with Russell was of major consequence for his intellectual career, for he focused upon set theory and its history, and also on the histories of mathematical analysis and of logic, and aspects of the history and philosophy of mechanics and of science.1 He corresponded at length with Russell until his death in 1919; the exchange forms the core of my book on their relationship.2 From his youth Jourdain suTered from a creeping paralysis called “Friedreich ’s ataxia”. It prevented him from taking the Part 2 Tripos; thus he did not graduate as a Wrangler and so could not compete for a fellowship at Trinity. So he made his living from a few scholarships and from freelance writing as an June 25, 2012 (9:21 pm) E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1 060 red.wpd 70 i. grattan-guinness 3 E. Zermelo, “Beweis, dass jede Menge wohlgeordnet werden kann”, Mathematische Annalen 59 (1904): 514–16. 4 See especially H. Rubin and J.yE Rubin, Equivalents of the Axiom of Choice, 2nd ed. (Amsterdam: North-Holland, 1985). 5 The history of this/these axioms has been charted in much detail. See especially J. Cassinet and M. Guillemot, “L’axiome du choix dans les mathématiques de Cauchy (1821) à Gödel (1940)”, 2 vols. (U. of Toulouse double docteur d’état des sciences, 1983); F.yA. MedvedeT, Rannyaya istoriya aksiomi vibora (Moscow: Nauka, 1982); and G.yH. Moore, Zermelo’s Axiom of Choice … (New York: Springer, 1982). RJ discusses the axioms in the contexts of the correspondence. independent scholar. In particular, the American house The Open Court Publishing Company employed him, especially from 1912 on their principal journal The Monist, commissioning papers (and also some books) from colleagues, in particular Russell. He seems to have served as its general editor soon after the death in February 1919 of its founder editor, Paul Carus, but he died himself early in October. Those last months form the time-frame of this paper. 2.wobsession Jourdain’s principal research interest in the foundations of mathematics came to focus upon the denumerable “axiom of choice” in set theory and mathematics , as Ernst Zermelo named it a few years after introducing it in 1904.3 Take an inWnite ensemble of non-empty and pairwise disjoint sets and choose a member from each set in independent actions; then the axiom asserts that the collection of chosen members can always be regarded as a genuine set. But this manner of forming a set roused considerable doubts and opposition among many (though not all) set-theorists and logicians. Some of them rejected the axiom altogether; others tried to reprove theorems that used the axiom by proofs that avoided it; several sought hopefully more congenial assumptions that were logically equivalent to the axiom, and eventually many came to light.4 Logicists such...