Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    It redirected philosophical attention to neglected questions of natural and metaphysical necessity and to the connections between these and theories of reference, in particular of naming, and of identity. From a critique of the dominant tendency to assimilate names to descriptions and more generally to treat their reference as a function of their Fregean sense, surprisingly deep and widespread consequences may be drawn. The largely discredited distinction between accidental and essential properties, both of individual things (including people) and of kinds of things, is revived. So is a consequent view of science as what seeks out the essences of natural kinds. Traditional objections to such views are dealt with by sharpening distinctions between epistemic and metaphysical necessity; in particular by the startling admission of necessary a posteriori truths. From these, in particular from identity statements using rigid designators whether of things or of kinds, further remarkable consequences are drawn for the natures of things, of people, and of kinds; strong objections follow, for example to identity versions of materialism as a theory of the mind.This seminal work, to which today's thriving essentialist metaphysics largely owes its impetus, is here published with a substantial new Preface by the author.

    Written in short, carefully numbered paragraphs of extreme brilliance, it captured the imagination of a generation of philosophers. For Wittgenstein, logic was something we use to conquer a reality which is in itself both elusive and unobtainable. He famously summarized the book in the following words: 'What can be said at all can be said clearly; and what we cannot talk about we must pass over in silence.' David Pears and Brian McGuinness received the highest praise for their meticulous translation. The work is prefaced by Bertrand Russell's original introduction to the first English edition.

    At the same time adjacent portions of philosophy and logic are discussed. To the existence of what objects may a given scientific theory be said to be committed? And what considerations may suitably guide us in accepting or revising such ontological commitments? These are among the questions dealt with in this book, particular attention being devoted to the role of abstract entities in mathematics. There is speculation on the mechanism whereby objects of one sort or another come to be posited a process in which the notion of identity plays an important part."This volume of essays has a unity and bears throughout the imprint of Quine's powerful and original mind. It is written with the felicity in the choice of words which makes everything that Quine writes a pleasure to read, and which ranks him among the best contemporary writers on abstract subjects." (Cambridge Review)"Professor Quine's challenging and original views are here for the first time presented as a unity. The chief merit of the book is the heart-searching from which it arose and to which it will give rise. In vigour, conciseness, and clarity, it is characteristic of its author." (Oxford Magazine)

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Topics: elimination of metaphysics, function of philosophy, nature of philosophical analysis, the a priori, truth & probability, critique of ethics & theology, self & the common world etc.IntroductionThe elimination of metaphysicsThe function of philosophy The nature of philosophical analysisThe a priori Truth & probabilityCritique of ethics & theologyThe self & the common worldSolutions of outstanding philosophical disputesIndex

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    Ryle's linguistic analysis remaps the conceptual geography of mind, not so much solving traditional philosophical problems as dissolving them into the mere consequences of misguided language. His plain language and esstentially simple purpose place him in the traditioin of Locke, Berkeley, Mill, and Russell.

    It remains the one of the most widely read books about science to come out of the twentieth century.(Note: the book was first published in 1934, in German, with the title Logik der Forschung. It was "reformulated" into English in 1959. See Wikipedia for details.)

    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.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

    In addition, the wide range of Leibniz's work--letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period--heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

    

    Richard Rorty, a Princeton professor who had contributed to the analytic tradition in philosophy, was now attempting to shrug off all the central problems with which it had long been preoccupied. After publication, the Press was barely able to keep up with demand, and the book has since gone on to become one of its all-time best-sellers in philosophy. Rorty argued that, beginning in the seventeenth century, philosophers developed an unhealthy obsession with the notion of representation. They compared the mind to a mirror that reflects reality. In their view, knowledge is concerned with the accuracy of these reflections, and the strategy employed to obtain this knowledge--that of inspecting, repairing, and polishing the mirror--belongs to philosophy. Rorty's book was a powerful critique of this imagery and the tradition of thought that it spawned. He argued that the questions about truth posed by Descartes, Kant, Hegel, and modern epistemologists and philosophers of language simply couldn't be answered and were, in any case, irrelevant to serious social and cultural inquiry. This stance provoked a barrage of criticism, but whatever the strengths of Rorty's specific claims, the book had a therapeutic effect on philosophy. It reenergized pragmatism as an intellectual force, steered philosophy back to its roots in the humanities, and helped to make alternatives to analytic philosophy a serious choice for young graduate students. Twenty-five years later, the book remains a must-read for anyone seriously concerned about the nature of philosophical inquiry and what philosophers can and cannot do to help us understand and improve the world.