In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    For this question and other ones like it have been the stuff of philosophical rumination from Plato to Popper. In a series of accessible and engagingly written essays, "50 Philosophy Ideas You Really Need to Know" introduces and explains the problems of knowledge, consciousness, identity, ethics, belief, justice and aesthetics that have engaged the attention of thinkers from the era of the ancient Greeks to the present day.

    Schopenhauer's perception of the importance of art, morality and self awareness in a blind struggle against a Godless, meaningless world radically transformed our understanding of the individual and remains a searing vision of the human condition.

    Explaining how such basic concepts as number and magnitude, space and force were developed, the great French mathematician refutes the skeptical position that modern scientific method and its results are wholly factitious. The places of rigorous logic and intuitive leaps are both established by an analysis of contrasting methods of idea-creation in individuals and in modern scientific traditions. The nature of hypothesis and the role of probability are investigated with all of Poincaré's usual fertility of insight.Partial contents: On the nature of mathematical reasoning. Magnitude and experiment. Space: non-Euclidean geometrics, space and geometry, experiment and geometry. Force: classical mechanics, relative and absolute motion, energy and thermodynamics. Nature: hypotheses in physics, the theories of modern physics, the calculus of probabilities, optics and electricity, electro-dynamics."Poincaré's was the last man to take practically all mathematics, both pure and applied as his province. Few mathematicians have had the breadth of philosophic vision that Poincaré's had, and none is his superior in the gift of clear exposition." — Men of Mathematics, Eric Temple Bell, Professor of Mathematics, University of Cambridge

    Hollingdale with an introduction by Michael Tanner in Penguin Classics.Beyond Good and Evil confirmed Nietzsche's position as the towering European philosopher of his age. The work dramatically rejects the tradition of Western thought with its notions of truth and God, good and evil. Nietzsche demonstrates that the Christian world is steeped in a false piety and infected with a 'slave morality'. With wit and energy, he turns from this critique to a philosophy that celebrates the present and demands that the individual imposes their own 'will to power' upon the world.This edition includes a commentary on the text by the translator and Michael Tanner's introduction, which explains some of the more abstract passages in Beyond Good and Evil.Frederich Nietzsche (1844-1900) became the chair of classical philology at Basel University at the age of 24 until his bad health forced him to retire in 1879. He divorced himself from society until his final collapse in 1899 when he became insane. A powerfully original thinker, Nietzsche's influence on subsequent writers, such as George Bernard Shaw, D.H. Lawrence, Thomas Mann and Jean-Paul Sartre, was considerable.If you enjoyed Beyond Good and Evil you might like Nietzsche's Thus Spoke Zarathustra, also available in Penguin Classics."One of the greatest books of a very great thinker." —Michael Tanner

    On its appearance in 1946 the book quickly became the focus of controversy.Polanyi aims to show that science must be understood as a community of inquirers held together by a common faith; science, he argues, is not the use of "scientific method" but rather consists in a discipline imposed by scientists on themselves in the interests of discovering an objective, impersonal truth. That such truth exists and can be found is part of the scientists' faith. Polanyi maintains that both authoritarianism and scepticism, attacking this faith, are attacking science itself.

    "Shapin's account is informed, nuanced, and articulated with clarity. . . . This is not to attack or devalue science but to reveal its richness as the human endeavor that it most surely is. . . .Shapin's book is an impressive achievement."—David C. Lindberg, Science"Shapin has used the crucial 17th century as a platform for presenting the power of science-studies approaches. At the same time, he has presented the period in fresh perspective."—Chronicle of Higher Education"Timely and highly readable . . . A book which every scientist curious about our predecessors should read."—Trevor Pinch, New Scientist"It's hard to believe that there could be a more accessible, informed or concise account of how it [the scientific revolution], and we have come to this. The Scientific Revolution should be a set text in all the disciplines. And in all the indisciplines, too."—Adam Phillips, London Review of Books"Shapin's treatise on the currents that engendered modern science is a combination of history and philosophy of science for the interested and educated layperson."—Publishers Weekly"Superlative, accessible, and engaging. . . . Absolute must-reading."—Robert S. Frey, Bridges"This vibrant historical exploration of the origins of modern science argues that in the 1600s science emerged from a variety of beliefs, practices, and influences. . . . This history reminds us that diversity is part of any intellectual endeavor."—Choice"Most readers will conclude that there was indeed something dramatic enough to be called the Scientific Revolution going on, and that this is an excellent book about it."—Anthony Gottlieb, The New York Times Book Review

    In this book Saul Kripke brings his powerful philosophic intelligence to bear on Wittgenstein's analysis of the notion of following a rule.

    It is often rational to act against our own best interests, he argues, and most of us have moralviews that are self-defeating. We often act wrongly, although we know there will be no one with serious grounds for complaint, and when we consider future generations it is very hard to avoid conclusions that most of us will find very disturbing.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    Barrett speaks eloquently and directly to concerns of the 1990s: a period when the irrational and the absurd are no better integrated than before and when humankind is in even greater danger of destroying its existence without ever understanding the meaning of its existence.Irrational Man begins by discussing the roots of existentialism in the art and thinking of Augustine, Aquinas, Pascal, Baudelaire, Blake, Dostoevski, Tolstoy, Hemingway, Picasso, Joyce, and Beckett. The heart of the book explains the views of the foremost existentialists--Kierkegaard, Nietzsche, Heidegger, and Sartre. The result is a marvelously lucid definition of existentialism and a brilliant interpretation of its impact.

    The essays deal with such central topics as freedom of the will, moral responsibility, the concept of a person, the structure of the will, the nature of action, the constitution of the self, and the theory of personal ideals. By focusing on the distinctive nature of human freedom, Professor Frankfurt is able to explore fundamental problems of what it is to be a person and of what one should care about in life.

    Slavoj Žižek has identified the four horsemen of this coming apocalypse: the worldwide ecological crisis; imbalances within the economic system; the biogenetic revolution; and exploding social divisions and ruptures. But, he asks, if the end of capitalism seems to many like the end of the world, how is it possible for Western society to face up to the end times? In a major new analysis of our global situation, Slavok Žižek argues that our collective responses to economic Armageddon correspond to the stages of grief: ideological denial, explosions of anger and attempts at bargaining, followed by depression and withdrawal. After passing through this zero-point, we can begin to perceive the crisis as a chance for a new beginning. Or, as Mao Zedong put it, “There is great disorder under heaven, the situation is excellent.” Slavoj Žižek shows the cultural and political forms of these stages of ideological avoidance and political protest, from New Age obscurantism to violent religious fundamentalism. Concluding with a compelling argument for the return of a Marxian critique of political economy, Žižek also divines the wellsprings of a potentially communist culture—from literary utopias like Kafka’s community of mice to the collective of freak outcasts in the TV series Heroes.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    The controversy surrounding these unsolved problems is as relevant to the psychology of cognitive development as it is to the philosophy of science. No serious student of either discipline can afford to misunderstand Goodman's classic argument.