The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.

The interpretation of indirect discourse is one of the most persistent and pervasive themes in post-Fregean semantics. Since Frege we have managed to learn a good deal about the workings of various technical approaches to indirect discourse, but fundamental philosophical issues have remained unresolved.

Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

Philosophers of modern logic have cherished no project more dearly than that of extensional reduction. Despite occasional protests that this project was ill-conceived from the start, or that it fails to account for important areas of experience and thought, the extensionalist mills have been grinding away anyhow. Their grinding has brought with it a number of important technical successes, replete with philosophical claims that light has finally been shed on areas hitherto buried in incomprehensible darkness.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This book changes your views on history, civilization, and the world. German philosopher and polymath Oswald Spengler displays his controversial opinions about world history. He defines "culture" as a superorganism which has a lifespan of birth, flourishing, and death, and defines "civilization" as the end-product of culture. He divides the entire history of the world into eight distinct cultures, from which all civilizations, religions, and wars arose. Spengler was criticized for his cataclysmic prediction of the downfall of western civilization in (...) the twenty first century, yet it's shocking to see markers for this prediction in everyday news. He claims that democracy is but the political weapon of money, and that media is the means through which money operates a democratic political system. According to him, the penetration of money's power through a society is one of many signs of the shift from "culture" to "civilization". After reading this, you'll be more learned in history, philosophy, science, mathematics, architecture, music, art, literature, and even Greek and Latin. "When the first volume of The Decline of the West appeared in Germany a few years ago, thousands of copies were sold. Cultivated European discourse quickly became Spengler-saturated. Spenglerism spurted from the pens of countless disciples. It was imperative to read Spengler, to sympathize or revolt. It still remains so." "When Oswald Spengler speaks, many a Western Worldling stops to listen." New York Times. (shrink)