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In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support....
The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet. The foundational debate is presented with all its brilliant contributions and its shortcomings, its new ideas and its misunderstandings.
Hellenistic philosophy concerns the thought of the Epicureans, Stoics, and Skeptics, the most influential philosophical groups in the era between the death of Alexander the Great (323 BCE) and the defeat of the last Greek stronghold in the ancient world (31 BCE). The Routledge Handbook of Hellenistic Philosophy provides accessible yet rigorous introductions to the theories of knowledge, ethics, and physics belonging to each of the three schools, explores the fascinating ways in which interschool rivalries shaped the philosophies of the era, and offers unique insight into the relevance of Hellenistic views to issues today, such as environmental ethics, consumerism, and bioethics. Eleven count...
What is a safe haven? What role should they play in an investment portfolio? Do we use them only to seek shelter until the passing of financial storms? Or are they something more? Contrary to everything we know from modern financial theory, can higher returns actually come as a result of lowering risk? In Safe Haven, hedge fund manager Mark Spitznagel—one of the top practitioners of safe haven investing and portfolio risk mitigation in the world—answers these questions and more. Investors who heed the message in this book will never look at risk mitigation the same way again.
1904-26 (includes lists of members)
Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought...
This book deals with central elements of the cultural, political and social background of Austrian economic theory in general and Menger's version of it in particular. It draws on Menger's theoretical writings as well as on his explicitly methodological works as source material.