Background
Karl Menger was born at Neusandez, in Galicia, on February 23, 1840.
(This volume brings together those papers of mine which ma...)
This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.
http://www.amazon.com/gp/product/9027703213/?tag=2022091-20
( One of the twentieth century's most original mathematic...)
One of the twentieth century's most original mathematicians and thinkers, Karl Menger taught students of many backgrounds. In this, his radical revision of the traditional calculus text, he presents pure and applied calculus in a unified conceptual frame, offering a thorough understanding of theory as well as of the methodology underlying the use of calculus as a tool. The most outstanding feature of this text is the care with which it explains basic ideas, a feature that makes it equally suitable for beginners and experienced readers. The text begins with a "mini-calculus" which brings out the fundamental results without recourse to the notions of limit and continuity. The standard subject matter is then presented as a pure and unambiguous calculus of functions. The issues surrounding the applications of pure calculus to problems in the sciences are faced in a forthright manner by carefully analyzing the meaning of "variable quantity" and clarified by resuscitating Newton's concept of fluents. The accompanying exercises are original, insightful and an integral part of the text. This Dover edition features a new Preface and Guide to Further Reading by Bert Schweizer and Abe Sklar.
http://www.amazon.com/gp/product/B00MS49N5Y/?tag=2022091-20
Karl Menger was born at Neusandez, in Galicia, on February 23, 1840.
He was educated at the Universities of Vienna and Prague.
In 1873 was appointed professor of economics at the University of Vienna. In 1900 he was made a member of the Austrian House of Peers and three years later retired from teaching to devote himself exclusively to research in political economy.
His doctrines resemble those of H. H. Gossen, W. S. Jevons, and Léon Walras, who at approximately the same time advanced similar ideas. Menger also opposed the historical method of research, advancing the concept, later developed by W. Windelband and H. Rickert, that theoretical and speculative research were equally valid.
His doctrine of money emphasized that fluctuations in the value of money were based on the cash balances of financial institutions and individuals.
He was the author of Grundsätze der Volkswirtschaftslehre (1871), Untersuchungen überuber die Methode der Socialwissenschaften, und der politischen Ökonomie insbesondere (1883), Die Irrthümer des Historismus in der Deutschen Nationalökonomie (1884), and the article on money in Handwörterbuch der Staatswissenschaften.
(This volume brings together those papers of mine which ma...)
( One of the twentieth century's most original mathematic...)