Essays on the Theory of Numbers.: I. Continuity and Irrational Numbers. II. The Nature and Meaning of Numbers. Authorized translation by Wooster Woodruff Beman.

Chicago: The Open Court Publishing Company,, 1901. A milestone of mathematical logic First edition in English, first printing, of the German mathematician's essays on the logical foundations of numerical systems. The two essays were originally published as "Stetigkeit und irrationale Zahlen" (1872) and "Was sind und was sollen die Zahlen?" (1888) and include the first discussion of the Dedekind cut, now the standard definition of real numbers. Dedekind (1831-1916) was a pioneer in the development of modern set theory and the philosophy of mathematics. He developed the present theories when he was lecturing in Zurich in 1858, during which he noted the need for a purely scientific foundation of arithmetic; the resulting essays constitute a significant moment in the shift from geometric to algebraic mathematical reasoning. They "exerted a strong influence on subsequent research in the foundations of mathematics" and "laid the foundations for much of modern-day real analysis and point-set topology" (Ewald, pp. 787 & 766). Provenance: with the ink ownership signature of "B. J. McCartin" on the front free endpaper. Brian J. McCartin (1951-2016) was Professor of Applied Mathematics at Kettering University. McCartin solved a problem of linear regression first noted by Sir Francis Galton by extending Karl Pearson's "geometrical solution to include unequal variances in the data [using] the ancient Greek geometry of the ellipse" (Hibbard, online). Octavo. Original red cloth, spine and front cover lettered in gilt, top edge gilt. With 4 pp. publisher's advertisements at rear. Contemporary ink ownership signature of one "Geo: Hurrell" dated August 1901 on front free endpaper. Covers marked, spine ends and corners slightly bumped, faint foxing to endpapers, residue from label removal to front pastedown, occasional pencil annotations to contents: a very good copy. William Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, vol. II, 1999; Dawn Hibbard, "100-year-old statistics problem solved - beautifully", Kettering University News, accessible online.