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Selected essays on the history of set theory and logics (1906-1918). (English) Zbl 0853.01037

Instrumenta Rationis. Sources for the History of Logic in the Modern Age. 6. Bologna: Cooperativa Libraria Universitaria Editrice Bologna, xlii, 352 p. (1991).
This is a reprint collection of Philipp E. B. Jourdain’s (1879-1919) pioneer studies on the history of logic and the foundations of arithmetic. The editor did a good service especially by putting together two series of articles, of which the first dealt with “The Development of the Theory of Transfinite Numbers”. In this series of articles published in four parts [Arch. Math. Phys. 10, 254-281 (1905-1906); 14, 289-311 (1908-1909); 16, 21-43 (1910); 22, 1-21 (1913-1914)] Jourdain focused on the growth of the theory of functions up to 1870, Karl Weierstrass’s theory of functions, and on the set theoretic foundations of transfinite numbers proposed by Georg Cantor. In the second series of articles Jourdain treated “The Development of the Theories of Mathematical Logic and the Principles of Mathematics” [Q. J. Pure Appl. Math. 41, 324-352 (1910); 43, 219-314 (1912); 44, 113-128 (1913)]. He thus attempted to write the history of a discipline which was then still in a dynamic process of constituting itself. Jourdain started his story with Leibniz, but he then concentrated on the development since Boole’s algebra of logic. Jourdain gave one of the earliest and even today very rare accounts of Hugh MacColl’s system of logic, and furthermore detailed descriptions of the logical systems of Frege, Peano and Jevons. The edition is complemented by a reprint of the booklet “The Philosophy of Mr. B*rtr*and R*ss*ll” which was edited by Jourdain in 1918 (Allen and Unwin, London) containing texts written by Jourdain, Bertrand Russel and (in an appendix) by Lewis Carroll on logic and the foundations of mathematics.
The book is opened by an informative introduction by the editor who had earlier published a commentary on the correspondence between Russell and Jourdain [Dear Russell – Dear Jourdain. A Commentary on Russell’s logic, based on his correspondence with Philip Jourdain (Duckworth, London; Columbia University Press, New York) (1977; Zbl 0369.01006)]. He surveys the biography of Jourdain and his “non-career” (p. xii) – Jourdain had to give up his studies at Trinity College, Oxford, due to a creeping paralysis. After having presented some essentials on Jourdain’s mathematical work which was inspired by the objective to prove the axiom of choice, the editor discusses Jourdain’s conversion to historical studies and sketches the contents of Jourdain’s essays adding some comments on their context and on recent studies on the topics treated. The book ends with indices of authors and subjects covering not only the introduction but also the reprinted texts.

MSC:

01A75 Collected or selected works; reprintings or translations of classics
03-03 History of mathematical logic and foundations

Keywords:

Essays; History; Logics

Citations:

Zbl 0369.01006
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