This volume contains two of his most important works: The Epitome of Copernican Astronomy (books 4 and 5 of which are translated here) is a textbook of Copernican science, remarkable for the prominence given to physical astronomy and for the extension to the Jovian system of the laws recently discovered to regulate the motions of the Planets. Harmonies of the World (book 5 of which is translated here) expounds an elaborate system of celestial harmonies depending on the varying velocities of the planets.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    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.

    Chown fearlessly addresses the big questions on the nature of the universe, the nature of reality, and the place of life in the universe. Ultimately, he says, science is about the down-to-earth things that matter to all of us. Where did the universe come from? Where did we come from? What the hell are we doing here?

    His fascinating quest draws on the history of philosophy, but also anthropology, sociology, psychology and neurology; he talks to theologians, priests, allegedly reincarnated Lamas, and delves into real-life cases of lost memory, personality disorders and personal transformation; and, candidly and engagingly, he describes his own experiences. After reading "The Ego Trick," you will never see yourself in the same way again.

    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

    Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. In fact, every major advance in his career came from this intuition: to assume that the universe embodies beautiful forms, forms whose hallmarks are symmetry—harmony, balance, proportion—and economy. There are other meanings of “beauty,” but this is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras, the ancient Greek who was the first to argue that “all things are number,” to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentiethcentury physics. Though the ancients weren’t right about everything, their ardent belief in the music of the spheres has proved true down to the quantum level. Indeed, Wilczek explores just how intertwined our ideas about beauty and art are with our scientific understanding of the cosmos.Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost literally the same equations that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries. The universe itself, suggests Wilczek, seems to want to embody beautiful and elegant forms. Perhaps this force is the pure elegance of numbers, perhaps the work of a higher being, or somewhere between. Either way, we don’t depart from the infinite and infinitesimal after all; we’re profoundly connected to them, and we connect them. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves.Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.

    How can it be possible that the world we see is not objective reality? And how can our senses be useful if they are not communicating the truth? Hoffman grapples with these questions and more over the course of this eye-opening work.Ever since Homo sapiens has walked the earth, natural selection has favored perception that hides the truth and guides us toward useful action, shaping our senses to keep us alive and reproducing. We observe a speeding car and do not walk in front of it; we see mold growing on bread and do not eat it. These impressions, though, are not objective reality. Just like a file icon on a desktop screen is a useful symbol rather than a genuine representation of what a computer file looks like, the objects we see every day are merely icons, allowing us to navigate the world safely and with ease.The real-world implications for this discovery are huge. From examining why fashion designers create clothes that give the illusion of a more “attractive” body shape to studying how companies use color to elicit specific emotions in consumers, and even dismantling the very notion that spacetime is objective reality, The Case Against Reality dares us to question everything we thought we knew about the world we see.

    "An excellent book presenting many of the major issues of ordinary language philosophy--very readable."--Mark Hamilton, Ashland University"The clarity, the wit, and the patience of the writing are liable to deceive the reader on only one point, namely the amount of hard work that lies behind these thoughts....This book is the one to put into the hands of those who have been over-impressed by Austin's critics....[Warnock's] brilliant editing puts everybody who is concerned with philosophical problems in his debt."--The Guardian

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    Book by Waring, Chris

    The long deconstructionist era was followed with a period dominated by Deleuze, which has in turn evolved into a new situation still difficult to define. However, one common thread running through the new brand of continental positions is a renewed attention to materialist and realist options in philosophy. Among the leaders of the established generation, this new focus takes numerous forms. It might be hard to find many shared positions in the writings of Badiou, DeLanda, Laruelle, Latour, Stengers, and i ek, but what is missing from their positions is an obsession with the critique of written texts. All of them elaborate a positive ontology, despite the incompatibility of their results. Meanwhile, the new generation of continental thinkers is pushing these trends still further, as seen in currents ranging from transcendental materialism to the London-based speculative realism movement to new revivals of Derrida. As indicated by the title The Speculative Turn, the new currents of continental philosophy depart from the text-centered hermeneutic models of the past and engage in daring speculations about the nature of reality itself. This anthology assembles authors, of several generations and numerous nationalities, who will be at the centre of debate in continental philosophy for decades to come.

    Throughout, the author provides a fair and balanced blending of the standard positions on epistemology with his own carefully reasoned positions or stances into the analysis of each concept. KEY TOPICS: Epistemological Questions. The Traditional Analysis of Knowledge. Modifying the Traditional Analysis of Knowledge. Evidentialist Theories of Justification. Non-evidentialist Theories of Knowledge and Justification. Skepticism. Epistemology and Science. Relativism. MARKET: For anyone interested in the philosophy of knowledge and rationality.

    The volume has three parts. The studies in the first part examine the history of hermeneutics, its central themes and the outstanding issues it has to confront. In Part II, Ricoeur's own current, constructive position is developed. A concept of the text is formulated as the implications of the theory are pursued into the domains of sociology, psychoanalysis and history. Many of the essays appear here in English for the first time; the editor's introduction brings out their background in Ricoeur's thought and the continuity of his concerns. The volume will be of great importance for those interested in hermeneutics and Ricoeur's contribution to it, and will demonstrate how much his approach offers to a number of disciplines.

    Over the next two decades, Copernicus expanded his theory through hundreds of observations, while compiling in secret a book-length manuscript that tantalized mathematicians and scientists throughout Europe. For fear of ridicule, he refused to publish.In 1539, a young German mathematician, Georg Joachim Rheticus, drawn by rumors of a revolution to rival the religious upheaval of Martin Luther's Reformation, traveled to Poland to seek out Copernicus. Two years later, the Protestant youth took leave of his aging Catholic mentor and arranged to have Copernicus's manuscript published, in 1543, as De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres)-the book that forever changed humankind's place in the universe.In her elegant, compelling style, Dava Sobel chronicles, as nobody has, the conflicting personalities and extraordinary discoveries that shaped the Copernican Revolution. At the heart of the book is her play And the Sun Stood Still, imagining Rheticus's struggle to convince Copernicus to let his manuscript see the light of day. As she achieved with her bestsellers Longitude and Galileo's Daughter, Sobel expands the bounds of narration, giving us an unforgettable portrait of scientific achievement, and of the ever-present tensions between science and faith.