By Morris Kline

"[Kline] is unfalteringly transparent in explaining mathematical principles; he's discovered yet no longer pedantic; he has ancient discernment, a sympathetic social outlook and a pleasant experience of enjoyable and irony.... the sweetness and fascination and infrequent excellence of arithmetic emerge from his tale. it's an exhilarating, provocative publication. - medical American"Still the simplest textbook for the heritage and philosophy of arithmetic for undergraduate liberal arts scholars. in particular strong for the age of the medical Revulution. - Janet A. Fitzgerald, Molloy university, NYProduct DescriptionThis booklet offers a remarkably wonderful account of the impacts arithmetic has exerted at the improvement of philosophy, the actual sciences, faith, and the humanities in Western existence.

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The method of trial and error may be direct but it may also be disastrous. Is experience the only way of obtaining knowledge? Not for beings endowed with a reasoning faculty. Reasoning can follow many routes, among which is the commonly traveled one of analogy. The Egyptians, for example, believed in immortality and so they buried their dead with clothes, utensils, jewelry, and other things that might be of use in the next world. Their reasoning was that since life on Earth required these articles, the after-life would also.

For example, some of the theorems established in geometries created during the last century contradict those proved by Euclid in his development of geometry. Though devoid of truth, mathematics has given man miraculous power over nature. The resolution of this greatest paradox in human thought will be one of our major concerns. Because the twentieth century must distinguish mathematical knowledge from truths it must also distinguish between mathematics and science, for science does seek truths about the physical world.

TRUE AND FALSE CONCEPTIONS 5 If mathematics is indeed a creative activity, what driving force causes men to pursue it? The most obvious, though not necessarily the most important, motive for mathematical investigations has been to answer questions arising directly out of social needs. Commercial and financial transactions, navigation, calendar reckoning, the construction of bridges, dams, churches, and palaces, the design of fortifications and weapons of warfare, and numerous other human pursuits involve problems that can best be resolved by mathematics.

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