From an Ivory Tower: A Discussion of Philosophical Problems Originating in Modern Mathematics

The Bruce Publishing Company, Published 1960. Hardcover, vii, 122 pp.; 22 cm; Impact Books series; copyright 1960, no later printing indicated; illustrated with geometric diagrams and tables. In Good condition, no dust jacket. Brown cloth boards with black lettering on spine, Impact Books device and publisher at foot of spine, blind-stamped device on front cover; mild to moderate shelf and edge wear, with scuffing and some color loss to front cover, heaviest around the device at lower right, and along corner tips. Binding tight. Endpapers moderately toned, with heavy offset browning to front and rear free endpapers and some foxing. Pages clean. Otherwise unmarked. Jesuit mathematician's answer to Morris R. Cohen and Max Black, who had argued from non-Euclidean geometry that no principle can be taken as self-evident, a challenge aimed squarely at the first principles of Catholic ethics. Written for nonmathematicians, it works from Euclid's Elements through Saccheri's attempted proof of the parallel postulate and the geometries of Gauss, Bolyai, Lobachevsky and Riemann, to Hilbert's postulates, Peano's counting numbers, transfinite numbers, group theory and the Boole-Schroeder algebra of classes, applied in the last chapter to the syllogism. Appendix gives Book I of Euclid's Elements. Part of Bruce's Impact Books, a series presenting work by scholars "both Catholic and non-Catholic" to the general reader. Contents: Preface; Euclidean Geometry; Non-Euclidean Geometry; The Problem of the Geometries; What Is Mathematics?; Modern Criticism of Euclid's Elements; The Numbers of Mathematics; Infinite Classes; The Boole-Schroeder Algebra; Applications of the Boole-Schroeder Algebra; Appendix: Euclid's Elements, Book I; Index.…