“We have no more beginnings,” George Steiner begins in this, his most radical book to date. A far-reaching exploration of the idea of creation in Western thought, literature, religion, and history, this volume can fairly be called a magnum opus. He reflects on the different ways we have of talking about beginnings, on the “core-tiredness” that pervades our end-of-the-millennium spirit, and on the changing grammar of our discussions about the end of Western art and culture. With his well-known elegance of style and intellectual range, Steiner probes deeply into the driving forces of the human spirit and our perception of Western civilization’s lengthening afternoon shadows. Roaming across topics as diverse as the Hebrew Bible, the history of science and mathematics, the ontology of Heidegger, and the poetry of Paul Celan, Steiner examines how the twentieth century has placed in doubt the rationale and credibility of a future tense—the existence of hope. Acknowledging that technology and science may have replaced art and literature as the driving forces in our culture, Steiner warns that this has not happened without a significant loss. The forces of technology and science alone fail to illuminate inevitable human questions regarding value, faith, and meaning. And yet it is difficult to believe that the story out of Genesis has ended, Steiner observes, and he concludes this masterful volume of reflections with an eloquent evocation of the endlessness of beginnings.

Relativity: A Richer Truth is a book written by Philipp Frank that explores the fundamental principles of Albert Einstein's theory of relativity. The book is a comprehensive guide that delves into the history and development of the theory, explaining the complex concepts and ideas in a clear and concise manner.The book is divided into two parts, with the first part focusing on the historical background of relativity and the second part delving into the mathematical and physical principles that underlie the theory. The author provides a detailed account of Einstein's life and work, tracing the evolution of his ideas and the scientific and philosophical debates that surrounded them.The second part of the book explores the mathematical and physical principles that form the foundation of relativity. The author explains the concepts of space-time, the equivalence principle, and the nature of gravity, among others, in a way that is accessible to readers with no prior knowledge of physics.In addition to providing a clear and comprehensive introduction to relativity, the book also highlights the broader implications of the theory for our understanding of the universe and our place within it. The author discusses the philosophical and cultural implications of relativity, exploring its impact on our concepts of time, space, and reality.Overall, Relativity: A Richer Truth is an engaging and informative book that offers readers a deeper understanding of one of the most important scientific theories of the modern era. It is a must-read for anyone interested in the history of science, physics, or the philosophical implications of relativity.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

2014 Reprint of Original 1960 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. "Epistemological Problems" is a milestone in Ludwig von Mises' groundbreaking development of praxeology. This important work contains foundational thoughts on his theory of human action, or "logic of action," which forms the "distinctive methodology of the Austrian School... Mises was not only the major architect and elaborator of this methodology, but also the economist who most fully and successfully applied it to the construction of economic theory" (Rothbard). Mises headed the Austrian School, which "celebrates freedom and the individual, rather than determinism and the collective... and explicitly rejects the idea that the natural sciences provide the proper model for economic analysis" (Shenoy et al., Towards a Theoretical Framework, 19, 19n). In establishing the school's epistemological foundations, Mises first began working on the subject in a series of articles published in the 1920s. He "collected and published them in his seminal philosophical and methodological work, "Grundprobleme der Nationalökonimie" in 1933," which was not translated into English until this edition. Here Mises presents "economics from the point of view of the philosophy of science, and the actual economic analysis of value and inconvertible capital." The first chapter of the book, "The Task and Scope of the Science of Human Action," evolved as the core of the system "Mises had been working on for years... He argued that economic laws were true a priori, on a par with the laws of logic and mathematics... [This] remained one of his most controversial tenets," in that it frames economic theory as addressing "acts of the real world, such as the one that human beings make choices. But the facts of this sort cannot be observed... Economics is not an empirical science in this sense, but it is a science nevertheless." To Mises "the epistemology of economics was not just an idle pastime for ivory tower intellectuals. It was of direct practical relevance." "Epistemological Problems" remains fundamental in establishing the "significance of economic calculation for the architecture of economic science." It is his most powerful and comprehensive elaboration of the span of economic science, arguing that errors of socialism, institutional racism, nationalism and other aspects of human society can be seen as a revolt against the distinctive rationality of economic logic and science. A work that "has lost nothing of its importance... Epistemological Problems contains a considerable amount of discussion that cannot be found in any other of his writings... in particular his critical discussion of the works of those thinkers to whom he felt the greatest intellectual affinity and intellectual debt: Carl Menger, Eugen von Bohm-Bawerk and Max Weber" (Hülsmann, Introduction, 2002 edition, 670-671, 948, xxix, lv).

This book is an original—the first-ever treatment of the mathematics of Luck. Setting out from the principle that luck can be measured by the gap between reasonable expectation and eventual realization, the book develops step-by-step a mathematical theory that accommodates the entire range of our pre-systematic understanding of the way in which luck functions in human affairs. In so moving from explanatory exposition to mathematical treatment, the book provides a clear and accessible account of the way in which luck assessment enters into the calculations of rational decision theory.

This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers.

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field , remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

EditorsG++ introduction Part I Philosophy of Mathematics 1 Infinite regress and foundations of mathematics 2 A renaissance of empiricism in the recent philosophy of mathematics? 3 Cauchy and the continuum: the significance of non-standard analysis for the history and philosophy of mathematics 4 What does a mathematical proof prove? 5 The method of analysis-synthesis Part II Critical Papers 6 The problem of appraising scientific theories: three approaches 7 Necessity, Kineale and Popper 8 Changes in the problem of inductive logic 9 On Popperian historiography 10 Anomalies versus G++crucial experimentsG++ 11 Understanding Toulmin Part III Science and Education 12 A letter to the director of the London School of Economics 13 The teaching of the history of science 14 The social responsibility of science References Lakatos bibliography Indexes.

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy." "["Philosophical Remarks] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's "The Analysis of Mind. He modifies the "Tractatus's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."--Robert Hoffman, "Philosophy "Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."--Leonard Linsky, American Philosophical Association

This analyzes in depth such topics logical compulsion & mathematical conviction; calculation as experiment; mathematical surprise, discovery, & invention; Russell's logic, Godel's theorem, cantor's diagonal procedure, Dedekind's cuts; the nature of proof & contradiction; & the role of mathematical propositions in the forming of concepts.Translator's NoteEditors' PrefaceThe TextIndex

Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.

Friedrich Waismann was born in Vienna in 1896 and lived there until the time of the Anschluss in 1938. From then until his death in 1959 he lived in England; this, apart from a brief period at Cambridge early on, was almost wholly at Oxford, \,Vhere he held the posts, first, or reader in the philosophy of mathematics and then of reader in the philosophy of science. He was of Jewish descent -his father being Russian, his mother German. He studied mathematics and physics at the University of Vienna and attended the lec­ tures of Hahn. Beginning his career as a teacher of mathematics he soon be­ came an unofficial assistant to Moritz Schlick. It was Schlick's concern to see that the new philosophical ideas developed by Wittgenstein from the time of his return to philosophy in the later 1920s were made public that de­ termined the subsequent shape of Waismann's activities. Until the out­ break of the war in 1939 his main task was the preparation of a book in which Wittgenstein's thought was to be systematically expounded. Be­ tween 1927 and 1935 this project was carried on in close personal conjunc­ tion with Wittgenstein. A first version of the planned book, Logik. Sprache. Philosophie seems to have been completed by 1931. A very differ­ ent version came to England with Waismann in 1938. It finally appeared, in an English translation, as Principles of Linguistic Philosophy.

Arabic contributions to medicine, mathematics, astronomy, and other fields have been extensively studied, yet Arabic logic has never been systematically investigated. In this book, Nicholas Rescher sheds new light on the major philosophical contribution of Arab logicians. He provides a historical account of the evolution of Arabic logic, from its inception in the early ninth century through the sixteenth century, when these tenets gained wide acceptance. The book also includes a bio-bibliography of 170 Arabic logicians, and a discussion of the place of each within the overall scheme of developments.

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