0.00. Apart from any evident utility as an economizer of thought and of calculation, there is, in the manifold interpretation of a system of postulates a wide philosophical significance.1 The numerous instances of this multiplicity of meaning that have been devised in geometry, are common knowledge; in arithmetic the comparatively fewer examples, among which the Theory of Ideals of Dedekind is the classic, do not seem to be so generally appreciated, possibly because they lie slightly to one side of the main progress of analysis, although, as asserted by some,2 arithmetic may be the proper foundation of all. The purpose of this paper is twofold; (i) To show, by several examples, that the postulates and processes of arithmetic admit of a multiplicity of interpretation, all examples to be simple and interconnected; (ii) To construct a self-contained arithmetical theory fcf. 0.01 (i)] of a large and important class of numerical functions, the theory to be so formed that the inter-relations
About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.
Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for * at
www.forgottenbooks.org 0.00. Apart from any evident utility as an economizer of thought and of calculation, there is, in the manifold interpretation of a system of postulates a wide philosophical significance.1 The numerous instances of this multiplicity of meaning that have been devised in geometry, are common knowledge; in arithmetic the comparatively fewer examples, among which the Theory of Ideals of Dedekind is the classic, do not seem to be so generally appreciated, possibly because they lie slightly to one side of the main progress of analysis, although, as asserted by some,2 arithmetic may be the proper foundation of all. The purpose of this paper is twofold; (i) To show, by several examples, that the postulates and processes of arithmetic admit of a multiplicity of interpretation, all examples to be simple and interconnected; (ii) To construct a self-contained arithmetical theory fcf. 0.01 (i)] of a large and important class of numerical functions, the theory to be so formed that the inter-relations
About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.
Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the difficult to read text. Read books online for * at
www.forgottenbooks.orgEric Temple Bell was born in 1883 in Aberdeen, Scotland. His early education was obtained in England. Coming to the United States in 1902, he entered Stanford University and took his A.B. degree in 1904. In 1908 he was teaching fellow at the University of Washington, where he took his A.M. degree in 1909. In 1911 he entered Columbia University, where he took his Ph.D. degree in 1912. He returned to the University of Washington as instructor in mathematics and became full professor in 1921. During the summers of 1924-28 he taught at the University of Chicago, and in 1926 (first half) at Harvard University, when he was appointed Professor of Mathematics at the California Institute of Technology.
Dr. Bell was a former President of the Mathematical Association of America, a former Vice President of the American Mathematical Society and of the American Association for the Advancement of Science. He was on the editorial staffs of the "Transactions of the American Mathematical Society," the "American Journal of Mathematics," and the "Journal of the Philosophy of Science." He belonged to The American Mathematical Society, the Mathematical Association of America, the Circolo Matematico di Palermo, the Calcutta Mathematical Society, Sigma Xi, and Phi Beta Kappa, and was a member of the National Academy of Sciences of the United States. He won the Bocher Prize of the American Mathematical Society for his research work. His twelve published books include "The Purple Sapphire" (1924), "Algebraic Arithmetic" (1927), "Debunking Science," and "Queen of the Sciences" (1931), "Numerology" (1933), and "The Search for Truth" (1934).
Dr. Bell died in December 1960, just before the publication ofhis latest book, "The Last Problem."
