Abraham A. Fraenkel was a world-renowned mathematician in pre–Second World War Germany, whose work on set theory was fundamental to the development of modern mathematics. A friend of Albert Einstein, he knew many of the era’s acclaimed mathematicians personally. He moved to Israel (then Palestine under the British Mandate) in the early 1930s. In his autobiography Fraenkel describes his early years growing up as an Orthodox Jew in Germany and his development as a mathematician at the beginning of the twentieth century. ​This memoir, originally written in German in the 1960s, has now been translated into English, with an additional chapter covering the period from 1933 until his death in 1965 written by the editor, Jiska Cohen-Mansfield. Fraenkel describes the world of mathematics in Germany in the first half of the twentieth century, its origins and development, the systems influencing it, and its demise. He also paints a unique picture of the complex struggles within the world of Orthodox Jewry in Germany. In his personal life, Fraenkel merged these two worlds during periods of turmoil including the two world wars and the establishment of the state of Israel. Including a new foreword by Menachem Magidor Foreword to the 1967 German edition by Yehoshua Bar-Hillel

In this work the distinguished physical chemist and philosopher, Michael Polanyi, demonstrates that the scientist's personal participation in his knowledge, in both its discovery and its validation, is an indispensable part of science itself. Even in the exact sciences, "knowing" is an art, of which the skill of the knower, guided by his personal committment and his passionate sense of increasing contact with reality, is a logically necessary part. In the biological and social sciences this becomes even more evident. The tendency to make knowledge impersonal in our culture has split fact from value, science from humanity. Polanyi wishes to substitute for the objective, impersonal ideal of scientific detachment an alternative ideal which gives attention to the personal involvement of the knower in all acts of understanding. His book should help to restore science to its rightful place in an integrated culture, as part of the whole person's continuing endeavor to make sense of the totality of his experience. In honor of this work and his The Study of Man Polanyi was presented with the Lecomte de Noüy Award for 1959.

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 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. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

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 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. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Commemorating Morton Deutsch's 95th birthday, this book presents ten major texts by this highly respected social psychologist on war and peace. This second volume presents Deutsch in his role as a leading social science activist on issues of war and peace - writing papers, making speeches and participating in demonstrations. After serving in the U.S. Air Force during World War II and being awarded two Distinguished Flying Cross medals, as a psychologist he was determined to work for a more peaceful world. Influenced by Kurt Lewin, who believed that nothing was as practical as a good theory, Deutsch pursued theoretical work on such issues as cooperation-competition, conflict resolution and social justice with regard to issues of war and peace. As President of the Society for the Study of Peace, Conflict and Violence, the Society for the Psychological Study of Social Issues and the International Society of Political Psychology, he helped to foster social science efforts to make for a more peaceful world.

"A major figure argues that the creation of bioethics was dependent on the rise of the post-WWII liberal democratic order and muses on the fate of the field, should that order fall"-- Provided by publisher.

The larger part of Yearbook 6 of the Institute Vienna Circle constitutes the proceedings of a symposium on Alfred Tarski and his influence on and interchanges with the Vienna Circle, especially those on and with Rudolf Carnap and Kurt Gödel. It is the first time that this topic has been treated on such a scale and in such depth. Attention is mainly paid to the origins, development and subsequent role of Tarski's definition of truth. Some contributions are primarily historical, others analyze logical aspects of the concept of truth. Contributors include Anita and Saul Feferman, Jan Wolenski, Jan Tarski and Hans Sluga. Several Polish logicians contributed: Gzegorczyk, Wójcicki, Murawski and Rojszczak. The volume presents entirely new biographical material on Tarski, both from his Polish period and on his influential career in the United States: at Harvard, in Princeton, at Hunter, and at the University of California at Berkeley. The high point of the analysis involves Tarski's influence on Carnap's evolution from a narrow syntactical view of language, to the ontologically more sophisticated but more controversial semantical view. Another highlight involves the interchange between Tarski and Gödel on the connection between truth and proof and on the nature of metalanguages. The concluding part of Yearbook 6 includes documentation, book reviews and a summary of current activities of the Institute Vienna Circle. Jan Tarski introduces letters written by his father to Gödel; Paolo Parrini reports on the Vienna Circle's influence in Italy; several reviews cover recent books on logical empiricism, on Gödel, on cosmology, on holistic approaches in Germany, and on Mauthner.

A great mathematician and teacher bridges the gap between science and the humanities in this exposition of the philosophy of science. Philipp Frank, a distinguished physicist and philosopher in his own right, traces the history of science from Aristotle to Einstein to illustrate philosophy’s ongoing role in the scientific process. Suitable for undergraduate students and other readers, this volume explains modern technology’s role in the gradual erosion of the rapport between physical theories and philosophical systems, and offers suggestions for restoring the link between these related areas. Dr. Frank examines the ancient Greek concept of natural science to illustrate the development of modern science; then, using geometry as an example, he charts its progress from Euclidean principles through the interpretations of Descartes, Mill, Kant, and the rise of four-dimensional and non-Euclidean geometry. Additional topics include the laws of motion, before and after innovations of Galileo and Newton; perceptions of motion, light, and relativity through the ages; metaphysical interpretations of relativistic physics; the motion of atomic objects and the phenomena and formulations of atomic physics; and the principle of causality and the validation of theories.

Paul R. Halmos, eminent mathematician and brilliant expositor, is also a snapshot addict. Between 1943 and 1988, Halmos photographed mathematicians, their spouses, their brothers and sisters and other relatives, their offices, their dogs, and their carillon towers. From the 6000 or so photographs in his collection, Halmos has chosen about 600 for this book. The pictures are candid shots showing mathematicians just being themselves. The accompanying captions, in addition to identifying the subjects, contain anecdotes and bits of history that reveal Halmos's inimitable wit, charm, and insight. This delightful collection of mathematical memorabilia has become a favorite browsing book as well as a valuable historical record. It is now available in a paperback edition.

This is a new release of the original 1955 edition.

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 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. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Demands of the Day asks about the logical standards and forms that should guide ethical and experimental anthropology in the twenty-first century. Anthropologists Paul Rabinow and Anthony Stavrianakis do so by taking up Max Weber’s notion of the “demands of the day.” Just as the demand of the day for anthropology decades ago consisted of thinking about fieldwork, today, they argue, the demand is to examine what happens after , how the experiences of fieldwork are gathered, curated, narrated, and ultimately made available for an anthropological practice that moves beyond mere ethnographic description. Rabinow and Stavrianakis draw on experiences from an innovative set of anthropological experiments that investigated how and whether the human and biological sciences could be brought into a mutually enriching relationship. Conceptualizing the anthropological and philosophic ramifications of these inquiries, they offer a bold challenge to contemporary anthropology to undertake a more rigorous examination of its own practices, blind spots, and capacities, in order to meet the demands of our day.

The concept of mass is one of the most fundamental notions in physics, comparable in importance only to those of space and time. But in contrast to the latter, which are the subject of innumerable physical and philosophical studies, the concept of mass has been but rarely investigated. Here Max Jammer, a leading philosopher and historian of physics, provides a concise but comprehensive, coherent, and self-contained study of the concept of mass as it is defined, interpreted, and applied in contemporary physics and as it is critically examined in the modern philosophy of science. With its focus on theories proposed after the mid-1950s, the book is the first of its kind, covering the most recent experimental and theoretical investigations into the nature of mass and its role in modern physics, from the realm of elementary particles to the cosmology of galaxies. The book begins with an analysis of the persistent difficulties of defining inertial mass in a noncircular manner and discusses the related question of whether mass is an observational or a theoretical concept. It then studies the notion of mass in special relativity and the delicate problem of whether the relativistic rest mass is the only legitimate notion of mass and whether it is identical with the classical (Newtonian) mass. This is followed by a critical analysis of the different derivations of the famous mass-energy relationship E = mc2 and its conflicting interpretations. Jammer then devotes a chapter to the distinction between inertial and gravitational mass and to the various versions of the so-called equivalence principle with which Newton initiated his Principia but which also became the starting point of Einstein's general relativity, which supersedes Newtonian physics. The book concludes with a presentation of recently proposed global and local dynamical theories of the origin and nature of mass. Destined to become a much-consulted reference for philosophers and physicists, this book is also written for the nonprofessional general reader interested in the foundations of physics.

In Memory of Emmy Noether.- 1. Über die Bildung des Formensystems der ternären biquadratischen Form.- 2. Über die Bildung des Formensystems der ternären biquadratischen Form.- 3. Zur Invariantentheorie der Formen von n Variabeln.- 4. Zur Invariantentheorie der Formen von n Variabeln.- 5. Rationale Funktionenkörper.- 6. Körper und Systeme rationaler Funktionen.- 7. Der Endlichkeitssatz der Invarianten endlicher Gruppen.- 8. Über ganze rationale Darstellung der Invarianten eines Systems von beliebig vielen Grundformen.- 9. Die allgemeinsten Bereiche aus ganzen transzendenten Zahlen.- 10. Die Funktionalgleichungen der isomorphen Abbildung.- 11. Gleichungen mit vorgeschriebener Gruppe.- 12. Invarianten beliebiger Differentialausdrücke.- 13. Invariante Variationsprobleme.- 14. Die arithmetische Theorie der algebraischen Funktionen einer Veränderlichen in ihrer Beziehung zu den iibrigen Theorien und zu der Zahlkörpertheorie.- 15. Die Endlichkeit des Systems der ganzzahligen Invarianten binärer Formen.- 16. Zur Reihenentwicklung in der Formentheorie.- 17. Gemeinsam mit W. Schmeidler: Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenäusdrticken.- 18. Über eine Arbeit des im Kriege gefallenen K. Hentzelt zur Eliminationstheorie.- 19. Idealtheorie in Ringbereichen.- 20. Ein algebraisches Kriterium für absolute Irreduzibilität.- 21. Formale Variationsrechnung und Differentialinvarianten.- 22. Bearbeitung von K. Hentzelt + Zur Theorie der Polynomideale und Resultanten.- 23. Algebraische und Differentialvarianten.- 24. Eliminationstheorie und allgemeine Idealtheorie.- 25. Eliminationstheorie und Idealtheorie.- 26. Abstrakter Aufbau der Idealtheorie im algebraischen Zahlkörper.- 27. Hilbertsche Anzahlen in der Idealtheorie.- 28. Gruppencharaktere und Idealtheorie.- 29. Der Endlichkeitssatz der Invarianten endlicher linearer Gruppen der Charakteristik p.- 30. Abstrakter Aufbau der Idealtheorie in algebraischen Zahl-und Funktionenkörpern.- 31. Der Diskriminantensatz für die Ordnungen eines algebraischen Zahl- oder Funktionenkörpers.- 32. Gemeinsam mit R. Brauer: Über minimale Zerfallungskörper irreduzibler Darstellungen.- 33. Hyperkomplexe GroBen und Darstellungstheorie in arithmetischer Auffassung.- 34. Hyperkomplexe Größen und Darstellungstheorie.- 35. Über Maximalbereiche aus ganzzahligen Funktionen.- 36. Idealdifferentiation und Differente.- 37. Normalbasis bei Körpern ohne höhere Verzweigung.- 38. Gemeinsam mit R. Brauer und H. Hasse: Beweis eines Hauptsatzes in der Theorie der Algebren.- 39. Hyperkomplexe Systeme in ihren Beziehungen zur kommutativen Algebra und zur Zahlentheorie.- 40. Nichtkommutative Algebren.- 41. Der Hauptgeschlechtssatz für relativ-galoissche Zahlkörper.- 42. Zerfallende verschränkte Produkte und ihre Maximalordnungen.- 43. Idealdifferentiation und Differente.- Algebra der hyperkomplexen Größen: Vorlesung von E. Noether, W. S. 1929/30. Ausgearbeitet von M. Deuring.- Notwendige und hinreichende Multiplizitätsbedingungen zum Noetherschen Fundamentalsatz der algebraischen Funktionen: von H. Kapferer (Mit einem Zusatz, gemeinsam mit E. Noether).- Bibliographie.- Liste der Kurzmitteilungen und Buchbesprechungen von Emmy Noether.