This fascinating exploration of the great discoveries of history's most important mathematicians seeks an answer to the eternal question: Does mathematics hold the key to understanding the mysteries of the physical world?

J. Robert Oppenheimer was one of the outstanding physicists of his generation. He was also an immensely gifted writer and speaker, who thought deeply about the way that scientific discoveries have changed the way people live and think. Displaying his subtlety of thought and expression as do few other documents, this book of his lectures discusses the moral and cultural implications of developments in modern physics. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book represents a new approach to philosophy. It treats philosophy as not a collection of systems, but as a study of problems. It recognizes in traditional philosophical systems the historical function of having asked questions rather than having given solutions. Professor Reichenbach traces the failures of the systems to psychological causes. Speculative philosophers offered answers at a time when science had not yet provided the means to give true answers. Their search for certainty and for moral directives led them to accept pseudo-solutions. Plato, Descartes, Spinoza, Kant, and many others are cited to illustrate the rationalist fallacy: reason, unaided by observation, was regarded as a source of knowledge, revealing the physical world and "moral truth." The empiricists could not disprove this thesis, for they could not give a valid account of mathematical knowledge. Mathematical discoveries in the early nineteenth century cleared the way for modern scientific philosophy. Its advance was furthered by discoveries in modern physics, chemistry, biology, and psychology. These findings have made possible a new conception of the universe and of the atom. The work of scientists thus altered philosophy completely and brought into being a philosopher with a new attitude and training. Instead of dictating so-called laws of reason to the scientist, this modern philosopher proceeds by analyzing scientific methods and results. He finds answers to the age-old questions of space, time, causality, and life; of the human observer and the external world. He tells us how to find our way through this world without resorting to unjustifiable beliefs or assuming a supernatural origin for moral standards. Philosophy thus is no longer a battleground of contradictory opinions, but a science discovering truth step by step. Professor Reichenbach, known for his many contributions to logic and the philosophy of science, addresses this book to a wider audience. He writes for those who do not have the leisure or preparation to read in the fields of mathematics, symbolic logic, or physics. Besides showing the principal foundations of the new philosophy, he has been careful to provide the necessary factual background. He has written a philosophical study, not a mere popularization. It contains within its chapters all the necessary scientific material in an understandable form—and, therefore, conveys all the information indispensable to a modern world-view. The late Hans Reichenbach was Professor of Philosophy at the University of California, Los Angeles. His previous books include

"Language is mankind's greatest invention--except, of course, that it was never invented." So begins linguist Deutscher's investigation into the genesis and evolution of language. If we started off with rudimentary utterances on the level of "man throw spear," how did we end up with sophisticated grammars, enormous vocabularies, and intricately nuanced degrees of meaning? Drawing on recent discoveries in linguistics, Deutscher exposes the elusive forces of creation at work in human communication, giving us fresh insight into how language emerges, evolves, and decays. He traces the evolution of linguistic complexity from an early "Me Tarzan" stage to such elaborate single-word constructions as the Turkish sehirlilestiremediklerimizdensiniz ("you are one of those whom we couldn't turn into a town dweller"). He shows how the processes of destruction and creation are continuously in operation, generating new words, new structures, and new meanings.--From publisher description.

"Circularity" is the story of a Janus-face conceptual structure, that on the one hand led to deep scientific discoveries, and on the other hand is used to trick the mind into believing the impossible. Alongside mathematical revolutions that eventually led to the invention of the computer, the book describes ancient paradoxes that arise from circular thinking. Another aspect of Circularity, its ability to entertain, leads to a surprising insight on the time old question " What is humor."

During the sixteenth and seventeenth centuries a radical change occurred in the patterns and framework of European thought. In the wake of Copernican theory and discoveries through the telescope, the notion of an ordered cosmos of "fixed stars" gave way to that of a universe infinite in both time and space-with significant and far-reaching consequences for human thought. Alexandre Koyré brilliantly interprets this revolution in terms of the change that occurred in our conception of the universe and our place in it, and illustrates the primacy of this change in the development of the modern world. "An important contribution to the problem of the transition from the world view characteristic of the medieval centuries to that which rapidly gained acceptance after the seventeenth century." (Philosophical Quarterly) "Koyré has provided the material and has illuminated it with uniformly perceptive and occasionally brilliant commentary.... An important contribution to the study of 17th-century thought." (Thomas S. Kuhn, Science) "A model of scholarliness without pedantry, of clarity without oversimplification." (Arthur Koestler, Encounter) "Surely a work that will be welcomed alike by the scientist, philosopher, and historian of ideas." (Philosophy and Phenomenological Research) Alexandre Koyré was a member of the Institute for Advanced Study, Princeton, and professor at the Ecole Pratique des Hautes Etudes in Paris. His books include Discovering Plato and Newtonian Studies.

Turok explores the transformative scientific discovers of the past three centuries, from classical mechanics to the nature of light and the evolution of the cosmos, and shows how they created shifts in the organization of society. He argues that we are on the cusp of another major transformation: the coming quantum revolution that will supplant our current digital age.

We often think of science as continuously advancing. In this collection of essays, five world-renowned writers explore obscure and neglected episodes in the history of science which suggest instead that the process of understanding the significance of scientific discoveries can be erratic, contradictory, even irrational. Jonathan Miller, Oliver Sacks, and Daniel Kevles show how promising new ideas may at first fail to be noticed or accepted, and then, years after they have been dismissed or forgotten, are recognized in a different form as important. R.C. Lewontin and Stephen Jay Gould discuss the ways that words and images used by scientists and popularizers alike, from the murals on the walls of natural history museums to such ubiquitous terms as "adaptation" and "environment," reflect serious and often unacknowledged distortions in the way we conceive of both individual organisms and the natural history of the world. These essays demonstrate that science is, in the words of Oliver Sacks, "a human enterprise through and through, an organic, evolving, human growth, with sudden spurts and arrests, and strange deviations, too. It grows out of its past, but never outgrows it, any more than we outgrow our childhood."

In this philosophical exploration of creativity, Irving Singer describes the many different types of creativity and their varied manifestations within and across all the arts and sciences. Singer's approach is pluralistic rather than abstract or dogmatic. His reflections amplify recent discoveries in cognitive science and neurobiology by aligning them with the aesthetic, affective, and phenomenological framework of experience and behavior that characterizes the human quest for meaning. Creativity has long fascinated Singer, and in Modes of Creativity he carries forward investigations begun in earlier works. Marshaling a wealth of examples and anecdotes ranging from antiquity to the present, about persons as diverse as Albert Einstein and Sherlock Holmes, Singer describes the interactions of the creative and the imaginative, the inventive, the novel, and the original. He maintains that our preoccupation with creativity devolves from biological, psychological, and social bases of our material being; that creativity is not limited to any single aspect of human existence but rather inheres not only in art and the aesthetic but also in science, technology, moral practice, as well as ordinary daily experience.