James R. Newman

From the Introduction. In 1931 there appeared in a German scientific periodical a relatively short paper with the forbidding title ""Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme"" (""On Formally Undecidable propositions of Principia Mathematica and Related Systems""). Its author was Kurt Godel, then a young mathematician of 25 at the University of Vienna and since 1938 a permanent member of the Institute for Advanced Study at Princeton. The paper is a milestone in the history of logic and mathematics. When Harvard University awarded Godel an honorary degree in 1952, the citation described the work as one of the most important advances in logic in modern times. At the time of its appearance, however, neither the title of Godel's paper nor its content was intelligible to most mathematicians.

The Point of it All is a thoroughly documented, researched book about the history of the designs of antique barbed fencing. This book describes hundreds of patents and over 2,000 patent design variations found in antique barbed fencing. Varieties such as mild steel barbed wire strands, sheet metal barbed strips, barbed metal rods, and barbed wooden rails. Antique barbed fencing evolved from the wooden fences and plain wire fences of the 1850s. The major antique barbed fencing period occurred from the late 1860s and mid-1870s to early 1900s when inventors in the Midwest and Northeast designed hundreds of new ways to corral livestock. Using US Patent and Trademark Office records and other information sources, the author describes how the inventors considered their patent designs unique, what their purpose was, and what factors influenced the changes in these designs over time. The author describes the common patterns found in the structure and form of these patent designs. Because of the complexity in these designs the author provides a proposed classification system for antique barbed fencing which can be used for sorting, organizing and indexing barbed fencing patents into similar patents and design groups. This book is intended for collectors, farm historians, and those of us who have ripped our pants crossing barbed wire fences.

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The GuardianIn 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. Kurt Godel (1906 – 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.

Sp testens seit Douglas R. Hofstadters "G del, Escher, Bach" ist der Name G del auch bei Nichtmathematikern bekannt geworden. 1931 hatte Kurt G del unter dem Titel " ber formal unterscheidbare S tze der Principia Mathematica und verwandter Systeme" seinen Unvollst ndigkeitssatz publiziert. Nagel und Newman haben das Wesentliche an G dels Ergebnissen f r Nichtfachleute dargestellt. Die vorliegende 9. Auflage ist ein unver nderter Nachdruck der l ngst klassisch gewordenen Ausgabe von 1958.

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

This book presents a readable explanation of Godel's theorem to both scholars and non-specialists. A combination of science and accessibility, it offers those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.

Vol. 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements, puzzles, and fancies. Individual contributions by A. M. Turing, Aldous Huxley, Sir James Jeans, Lewis Carroll, and other notables. Informative commentary by noted mathematics scholar James R. Newman precedes each essay. Numerous figures.

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.