Journal of the History of Philosophy

Nine Letters from Giuseppe Peano to Bertrand Russell H. C. KENNEDY INTRODUCTION PRESERVEDIN THEBERTRANDRUSSELLARCHIVESat McMaster University (Hamilton, Ontario) are nine letters from Giuseppe Peano to Bertrand Russell, covering the period from 1901 to 1912. ~The first was written only a few months after they met at the International Congress of Philosophy, Paris, 1900, and the last was written at the Frith International Congress of Mathematicians, Cambridge, 1912. This was a period of great change in the interests of Peano, a transition from the development and promotion of mathematical logic to his dedication to the ideal of an international auxiliary language. In 1900 he was the most prominent figure in the field of mathematical logic, but his accomplishments were in the preceding period. While Peano's interests waned, Russell's grew, and from the inspiration of meeting Peano (Russell wrote that the event "was a turning point in my intellectual development"2), Russell became, by 1912, the leader in this field. The correspondence presented here is one-sided, since we have only the letters Peano wrote to Russell. (The letters from Russell to Peano have apparently been lost.) Hence, we learn little of Russell, except for additional confirmation of his generosity. Nor, indeed , do the letters reveal a great deal about Peano, but this little is precious, since the documentary evidence of his life is sparse. It shows that, far from seeing Russell as a rival, Peano gladly recognized his accomplishments. We also get an echo of the opposition Peano met in his efforts to introduce his own language for scientific communication, when he mentions, in 1910 and again in 1912, that most people think it absurd. This opposition becomes a direct confrontation in the last letter. We present the letters first in English translation, followed by notes numbered to correspond to the letters, and then in the original language text. (Only obvious corrections of grammar and spelling have been made.) Providence College 1 I wish to thank Mr. Kenneth Blackwell, Archivist of the Bertrand Russell Archives, MeMaster University, Hamilton, Ontario, for very kindly furnishing copies of these letters, and Peano's nieces, Carola, Maria, and Caterina Peano, for permission to publish the writings of Peano. 2 B. Russell, The Autobiography of BertrandRussell:1872-1914 (Boston: Little, Brown and Company, 1967),p. 217. [205] 206 HISTORY OF PHILOSOPHY THE PEANO-RUSSELL LETTERS Turin, 19 March 1901 s Dear Sir: I shall publish directly your interesting memoir, which fills a gap between the work of Peirce and Schr/Sder on the one hand and the Formulaire on the other. Let me congratulate you on the facility and precision with which you manage the symbols of logic. Here are a few typogral~hical remarks. The notations R ~ do not pose serious typographical difficulties. Still, if you wish to write all the signs on the same line, you could replace them by Inv(erse) R, IR. The notation R ] of the Introduction au Formulaire (1894), p. 39, would now produce some confusion with the sign for substitution. The notation p to indicate the domain of R is clear, so long as the relation is indicated by a single letter. I am afraid there will be difficulties in indicating the domain of RS, R U S, R, i.e. relations indicated by a composite expression. Classes of pairs correspond to relations. YourP1 "4 Rerel. D: q p. =. 3 corresponds to 2 9 2 of w 3 (p. 28 of the Formulaire) 3 x33 y3[(x;y) ea].--. 3 y33 x3[(x;y) ea] May we represent your sign 6 by the letter Z turned 90 ~ and the sign ~ by T? The introduction of signs that are not in the typesetters' stock of ordinary or mathematical symbols causes long delays for the manufacture of new type. Sincerely yours, G. Peano Via Barbaroux 6. Turin, 27 May 19034 Esteemed colleague: Thank you for your book The Principles of Mathematics, which I have read in part a Russell's memoir, referred to in this letter, was submitted in the fall of 1900 and was published in the next issue of Peano's Rivista di Matematiea with the title, "Sur la logique des relations avec des applications/t la...