This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...) the first time. (shrink)

Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

Genevieve Lloyd presents a new study of the place of Enlightenment thought in intellectual history and of its continued relevance. She offers original readings of a range of key texts, which highlight the ways in which Enlightenment thinkers enacted in their writing--and reflected on--the interplay of intellect, imagination, and emotion.

For many of us, the great scientific discoveries of the modern age--the Big Bang, evolution, quantum physics, relativity--point to an existence that is bleak, devoid of meaning, pointless. But in The Sacred Depths of Nature, eminent biologist Ursula Goodenough shows us that the scientific world view need not be a source of despair. Indeed, it can be a wellspring of solace and hope. This eloquent volume reconciles the modern scientific understanding of reality with our timeless spiritual yearnings for reverence and (...) continuity. Looking at topics such as evolution, emotions, sexuality, and death, Goodenough writes with rich, uncluttered detail about the workings of nature in general and of living creatures in particular. Her luminous clarity makes it possible for even non-scientists to appreciate that the origins of life and the universe are no less meaningful because of our increasingly scientific understanding of them. At the end of each chapter, Goodenough's spiritual reflections respond to the complexity of nature with vibrant emotional intensity and a sense of reverent wonder. A beautifully written celebration of molecular biology with meditations on the spiritual and religious meaning that can be found at the heart of science, this volume makes an important contribution to the ongoing dialog between science and religion. This book will engage anyone who was ever mesmerized--or terrified--by the mysteries of existence. (shrink)

"One of the major works in the development of contemporary criticism and philosophy." -- J. Hillis Miller, Yale University Jacques Derrida's revolutionary theories about deconstruction, phenomenology, psychoanalysis, and structuralism, first voiced in the 1960s, forever changed the face of European and American criticism. The ideas in De la grammatologie sparked lively debates in intellectual circles that included students of literature, philosophy, and the humanities, inspiring these students to ask questions of their disciplines that had previously been considered improper. Thirty years (...) later, the immense influence of Derrida's work is still igniting controversy, thanks in part to Gayatri Spivak's translation, which captures the richness and complexity of the original. This corrected edition adds a new index of the critics and philosophers cited in the text and makes one of contemporary criticism's most indispensable works even more accessible and usable. (shrink)

Of fundamental importance to literary critics and philosophers, Difference and Repetition develops two central concepts -- pure difference and complex ...

Normativity concerns what we ought to think or do and the evaluations we make. For example, we say that we ought to think consistently, we ought to keep our promises, or that Mozart is a better composer than Salieri. Yet what philosophical moral can we draw from the apparent absence of normativity in the scientific image of the world? For scientific naturalists, the moral is that the normative must be reduced to the nonnormative, while for nonnaturalists, the moral is that (...) there must be a transcendent realm of norms. _Naturalism and Normativity_ engages with both sides of this debate. Essays explore philosophical options for understanding normativity in the space between scientific naturalism and Platonic supernaturalism. They articulate a liberal conception of philosophy that is neither reducible to the sciences nor completely independent of them—yet one that maintains the right to call itself naturalism. Contributors think in new ways about the relations among the scientific worldview, our experience of norms and values, and our movements in the space of reason. Detailed discussions include the relationship between philosophy and science, physicalism and ontological pluralism, the realm of the ordinary, objectivity and subjectivity, truth and justification, and the liberal naturalisms of Donald Davidson, John Dewey, John McDowell, and Ludwig Wittgenstein. (shrink)

At last available in paperback, this book anticipates and explains the post-structuralist turn to empiricism. Presenting a challenging reading of David Hume's philosophy, the work is invaluable for understanding the progress of Deleuze's thought.

Deleuze and Guattari differentiate between philosophy, science, and the arts - seeing each as a means of confronting chaos - and challenge the common view that philosophy is an extension of logic. The authors also discuss the similarities and distinctions between creative and philosophical writing. Fresh anecdotes from the history of philosophy illuminate this book, along with engaging discussions of composers, painters, writers, and architects.

This book comes to the rescue of scientific realism, showing that reports of its death have been greatly exaggerated. Philosophical realism holds that the aim of a particular discourse is to make true statements about its subject matter. Ilkka Niiniluoto surveys different kinds of realism in various areas of philosophy and then sets out his own critical realist philosophy of science.

Original essays by leading philosophers of science explore the question of whether metaphysics can and should be naturalized--conducted as part of natural science.

The late 20th century saw a remarkable flourishing of philosophy in France. The work of French philosophers is wide ranging, historically informed, often reaching out beyond the boundaries of philosophy; they are public intellectuals, taken seriously as contributors to debates outside the academy. Gary Gutting tells the story of the development of a distinctively French philosophy in the last four decades of the 20th century. His aim is to arrive at an account of what it was to 'do philosophy' in (...) France, what this sort of philosophizing was able to achieve, and how it differs from the analytic philosophy dominant in Anglophone countries. -/- His initial focus is on the three most important philosophers who came to prominence in the 1960s: Michel Foucault, Gilles Deleuze, and Jacques Derrida. He sets out the educational and cultural context of their work, as a basis for a detailed treatment of how they formulated and began to carry out their philosophical projects in the 1960s and 1970s. He gives a fresh assessment of their responses to the key influences of Hegel and Heidegger, and the fraught relationship of the new generation to their father-figure Sartre. He concludes that Foucault, Derrida, and Deleuze can all be seen as developing their fundamental philosophical stances out of distinctive readings of Nietzsche. The second part of the book considers topics and philosophers that became prominent in the 1980s and 1990s, such as the revival of ethics in Levinas, Derrida, and Foucault, the return to phenomenology and its use to revive religious experience as a philosophical topic, and Alain Badiou's new ontology of the event. Finally Gutting brings to the fore the meta-philosophical theme of the book, that French philosophy since the 1960s has been primarily concerned with thinking the impossible. (shrink)

Nietzsche called The Gay Science "the most personal of all my books." It was here that he first proclaimed the death of God -- to which a large part of the book is devoted -- and his doctrine of the eternal recurrence. Walter Kaufmann's commentary, with its many quotations from previously untranslated letters, brings to life Nietzsche as a human being and illuminates his philosophy. The book contains some of Nietzsche's most sustained discussions of art and morality, knowledge and truth, (...) the intellectual conscience and the origin of logic. Most of the book was written just before Thus Spoke Zarathustra, the last part five years later, after Beyond Good and Evil. We encounter Zarathustra in these pages as well as many of Nietzsche's most interesting philosophical ideas and the largest collection of his own poetry that he himself ever published. Walter Kaufmann's English versions of Nietzsche represent one of the major translation enterprises of our time. He is the first philosopher to have translated Nietzsche's major works, and never before has a single translator given us so much of Nietzsche. (shrink)

"God is dead. God remains dead. And we have killed him." This is the book in which Nietzsche put forth his boldest declaration. It is also his most personal. Essential reading for students of philosophy, history, and literature, it features some of Nietzsche's most important discussions of art, morality, knowledge, and, ultimately, truth.

" "Positions brings together three interviews with Derrida, outlining his central concerns and ideas.

In this outstanding collection of essays, Isaiah Berlin, one of the great thinkers of the twentieth century, discusses the importance in the history of thought of dissenters whose ideas still challenge conventional wisdom--among them Machiavelli, Vico, Montesquieu, Herzen, and Sorel. With his unusual powers of imaginative re-creation, Berlin brings to life original minds that swam against the current of their times.

What is empiricism and what could it be? Bas . van Fraassen, one of the world’s foremost contributors to philosophical logic and the philosophy of science, here undertakes a fresh consideration of these questions and offers a program for renewal of the empiricist tradition. The empiricist tradition is not and could not be defined by common doctrines, but embodies a certain stance in philosophy, van Fraassen says. This stance is displayed first of all in a searing, recurrent critique of metaphysics, (...) and secondly in a focus on experience that requires a voluntarist view of belief and opinion. Van Fraassen focuses on the philosophical problems of scientific and conceptual revolutions and on the not unrelated ruptures between religious and secular ways of seeing or conceiving of ourselves. He explores what it is to be or not be secular and points the way toward a new relationship between secularism and science within philosophy. (shrink)

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. (shrink)

This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.

Difficult Atheism shows how contemporary French philosophy is rethinking the legacy of the death of God in ways that take the debate beyond the narrow confines of atheism into the much broader domain of post-theological thinking. Christopher Watkin argues that Alain Badiou, Jean-Luc Nancy and Quentin Meillassoux each elaborate a distinctive approach to the post-theological, but that each approach still struggles to do justice to the death of God.

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)

Infinite Thought brings together a representative selection of the range of Alain Badiou's work, illustrating the power and diversity of his thought.

The subtractive : preface by Francois Wahl -- Philosophy itself -- The (re)turn of philosophy itself -- Definition of philosophy -- What is a philosophical institution? -- Philosophy and poetry -- The philosophical recourse to the poem -- Mallarm's method : subtraction and isolation -- Rimbaud's method : interruption -- Philosophy and mathematics -- Conference on subtraction -- Truth : forcing and unnameable -- Philosophy and politics -- Philosophy and love -- What is love? -- Philosophy and psychoanalysis -- Subject (...) and infinite -- Antiphilosophy : Lacan and Plato -- Writing of the generic -- Writing of the generic : Samuel beckett. (shrink)

Sam Gillespie's The Mathematics of Novelty presents a new account of Alain Badiou and Gilles Deleuze, identifying conceptual impasses in their philosophical ...

Early analytic philosophy -- Radical translation and intersubjective practice -- Critical outcome.

Every Thing Must Go aruges that the only kind of metaphysics that can contribute to objective knowledge is one based specifically on contemporary science as it ...

This volume, assembled with the collaboration of the author, presents for the first time in English a comprehensive outline of Badiou's ambitious system.

This volume presents a group of leading thinkers who criticize scientific naturalism not in the name of some form of supernaturalism, but in order to defend a ...

Derrida's introduction to his French translation of Husserl's essay "The Origin of Geometry," arguing that although Husserl privileges speech over writing in an account of meaning and the development of scientific knowledge, this privilege is in fact unstable.

Through the use of such "folk" concepts as belief, desire, intention, and expectation, Daniel Dennett asserts in this first full scale presentation of...

Are there really beliefs? Or are we learning (from neuroscience and psychology, presumably) that, strictly speaking, beliefs are figments of our imagination, items in a superceded ontology? Philosophers generally regard such ontological questions as admitting just two possible answers: either beliefs exist or they don't. There is no such state as quasi-existence; there are no stable doctrines of semi-realism. Beliefs must either be vindicated along with the viruses or banished along with the banshees. A bracing conviction prevails, then, to the (...) effect that when it comes to beliefs (and other mental items) one must be either a realist or an eliminative materialist. (shrink)

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

The history of Pythagoreanism is littered with different and incompatible interpretations. This observation directs this book towards a fundamentally historiographical rather than philological approach, setting out to reconstruct the way in which the tradition established Pythagoreanism s image.".