Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous.

This book draws its inspiration from Hilbert, Wittgenstein, Cavaillès and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question (...) it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences. (shrink)

The Cartesian method, construed as a way of organizing domains of knowledge according to the "order of reasons," was a powerful reductive tool. Descartes made significant strides in mathematics, physics, and metaphysics by relating certain complex items and problems back to more simple elements that served as starting points for his inquiries. But his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of (...) ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the negative and positive impact of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry, the Principles, the Treatise of Man, and the Meditations. (shrink)

This book explicates Leibnizian analysis as a search for conditions of intelligibility, and reconsiders his use of principles and methods as well as his account of truth in this way. Via careful reading of well-known, lesser known, and previously unedited texts, it gives a more accurate picture of his philosophical intentions, as well as the relevance of his project to contemporary debate. Two case studies are included, one concerning logic and the other arithmetic; they illustrate a theory of intelligibility that (...) takes as its central notion "possibility for thought", a notion which allows Leibniz to escape certain traps of psychologism, the pseudo-ontology of empiricism, and the empty forms of logicism, and suggests new approaches for contemporary philosophy. "In this remarkable study, Grosholz and Yakira offer a fresh interpretive and conceptual angle on Leibniz's metaphysics. [...] this study deserves high marks for its subtlety, novelty, and creative insight into Leibniz's modes of inquiry as well as for its philosophical acumen." Annals of Science. (shrink)

This book deals with a topic that has been largely neglected by philosophers of science to date: the ability to refer and analyze in tandem. On the basis of a set of philosophical case studies involving both problems in number theory and issues concerning time and cosmology from the era of Galileo, Newton and Leibniz up through the present day, the author argues that scientific knowledge is a combination of accurate reference and analytical interpretation. In order to think well, we (...) must be able to refer successfully, so that we can show publicly and clearly what we are talking about. And we must be able to analyze well, that is, to discover productive and explanatory conditions of intelligibility for the things we are thinking about. The book’s central claim is that the kinds of representations that make successful reference possible and those that make successful analysis possible are not the same, so that significant scientific and mathematical work typically proceeds by means of a heterogeneous discourse that juxtaposes and often superimposes a variety of kinds of representation, including formal and natural languages as well as more iconic modes. It demonstrates the virtues and necessity of heterogeneity in historically central reasoning, thus filling an important gap in the literature and fostering a new, timely discussion on the epistemology of science and mathematics. (shrink)

Most discussions of Leibniz's metaphysics of time and space begin and end with the correspondence between Leibniz and Samuel Clarke, Newton's friend and defender. But Leibniz's ideas about time and space are far richer than this exchange suggests, and Michael Futch shows that the study of those investigations will enhance current discussion among philosophers and cosmologists. Futch's scholarly attention to a wide range of texts is matched by his philosophical acuity. His detailed expositions of texts are not tedious or pedantic (...) because he never fails to bring out their philosophical interest and pertinence. So, too, the book's bibliography is especially valuable.The book opens with a discussion of Newton's substantivalism, which treats time and space as substance-like structures that exist independent of the objects located in them, versus Leibniz's reductionism, which holds time and space to be merely relations, ontologically dependent on the things that exist: space is the order of coexistences, time the order of successions. Futch gives useful historical background that explains why the debate takes the form that it does and what. (shrink)

The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VIVII of Platos Republic and Aristotles Prior and Posterior Analytics, to Kants Critique of Pure Reason and Mills A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers by Bertrand Russell. However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from (...) knowledge. This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. (shrink)

Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers (...) by Bertrand Russell (Logic and Knowledge. Essays, 1901–1950). However, it has remained an underdeveloped theme in the last century, because logic has been treated as separate from knowledge. -/- This book does not hope to make up for a century-long absence of discussion. Rather, its ambition is to call attention to the theme and stimulating renewed reflection upon it. The book collects essays of leading figures in the field and it addresses the theme as a topic of current debate, or as a historical case study, or when appropriate as both. Each essay is followed by the comments of a younger discussant, in an attempt to transform what might otherwise appear as a monologue into an ongoing dialogue; each section begins with an historical essay and ends with an essay by one of the editors. -/- Carlo Cellucci is Emeritus Professor of Philosophy at the University of Rome ‘La Sapienza,’ Italy. He is currently completing a book entitled, Remaking Logic: What is Logic Really? -/- Emily Grosholz is Professor of Philosophy at the Pennsylvania State University, USA. She is the author of Representation and Productive Ambiguity in Mathematics and the Sciences (Oxford University Press, 2007). -/- Emiliano Ippoliti is a Research Fellow at the University of Rome ‘La Sapienza,’ Italy. His main interests are heuristics, the logic of discovery, and problem-solving. He is currently working on a book, Ampliating Knowledge: Data, Hypotheses and Novelty. -/- TABLE OF CONTENTS -/- Foreword .................................................................................................... ix Acknowledgements ................................................................................. xxv -/- Section I: Logic and Knowledge -/- Chapter One................................................................................................. 3 The Cognitive Importance of Sight and Hearing in Seventeenthand Eighteenth-Century Logic (Mirella Capozzi) Discussion .............................................................................................. 26 (Chiara Fabbrizi) Chapter Two .............................................................................................. 33 Nominalistic Content (Jody Azzouni) Discussion ............................................................................................... 52 (Silvia De Bianchi) Chapter Three ............................................................................................ 57 A Garden of Grounding Trees (Göran Sundholm) Discussion.......................................................................................... .. 75 (Luca Incurvati) Chapter Four .............................................................................................. 81 Logics and Metalogics (Timothy Williamson) Discussion.......................................................................................... 101 (Cesare Cozzo) Chapter Five ............................................................................................ 109 Is Knowledge the Most General Factive Stative Attitude? (Cesare Cozzo) Discussion.......................................................................................... 117 (Timothy Williamson) Chapter Six .............................................................................................. 123 Classifying and Justifying Inference Rules (Carlo Cellucci) Discussion.......................................................................................... 143 (Norma B. Goethe) -/- Section II: Logic and Science -/- Chapter Seven.......................................................................................... 151 The Universal Generalization Problem and the Epistemic Status of Ancient Medicine: Aristotle and Galen (Riccardo Chiaradonna) Discussion.......................................................................................... 168 (Diana Quarantotto) Chapter Eight........................................................................................... 175 The Empiricist View of Logic (Donald Gillies) Discussion.......................................................................................... 191 (Paolo Pecere) Chapter Nine............................................................................................ 197 Artificial Intelligence and Evolutionary Theory: Herbert Simon’s Unifying Framework (Roberto Cordeschi) Discussion.......................................................................................... 216 (Francesca Ervas) Chapter Ten ............................................................................................. 221 Evolutionary Psychology and Morality: The Renaissance of Emotivism? (Mario De Caro) Discussion.......................................................................................... 232 (Annalisa Paese) Chapter Eleven ........................................................................................ 237 Between Data and Hypotheses (Emiliano Ippoliti) Discussion.......................................................................................... 262 (Fabio Sterpetti) -/- Section III: Logic and Mathematics -/- Chapter Twelve ....................................................................................... 273 Dedekind Against Intuition: Rigor, Scope and the Motives of his Logicism (Michael Detlefsen) Discussion.......................................................................................... 290 (Marianna Antonutti) Chapter Thirteen...................................................................................... 297 Mathematical Intuition: Poincaré, Polya, Dewey (Reuben Hersh) Discussion.......................................................................................... 324 (Claudio Bernardi) Chapter Fourteen ..................................................................................... 329 On the Finite: Kant and the Paradoxes of Knowledge (Carl Posy) Discussion.......................................................................................... 358 (Silvia Di Paolo) Chapter Fifteen ........................................................................................ 363 Assimilation: Not Only Indiscernibles are Identified (Robert Thomas) Discussion.......................................................................................... 380 (Diego De Simone) Chapter Sixteen ....................................................................................... 385 Proofs and Perfect Syllogisms (Dag Prawitz) Discussion.......................................................................................... 403 (Julien Murzi) Chapter Seventeen ................................................................................... 411 Logic, Mathematics, Heterogeneity (Emily Grosholz) Discussion.......................................................................................... 427 (Valeria Giardino) -/- Contributors........................................................................................ ..... 433 Index............................................................................................... ......... 437 -/- Price Uk Gbp: 49.99 Price Us Usd: 74.99. 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Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

During the past few decades, philosophers of biology have debated the issue of reductionism versus anti-reductionism, with both sides often claiming a ‘pluralist’ position. However, both sides also tend to focus on a single research paradigm, which analyzes living things in terms of certain macromolecular components. I offer a case study where biologists pursue other analytic pathways, in a tradition of quantitative genetics that originates with the initially purely mathematical theories of R. A. Fisher, J. B. S. Haldane, and Sewall (...) Wright in the 1930s. Aster Models offers a class of statistical models designed for studying the fitness of plant and animal populations, by integrating the measurements of separate, sequential, non-normally distributed fitness components in novel ways. Their work generates important theoretical and practical results that do not require elaboration by molecular biology, and thus serves as a counterexample to the claims of philosophers whose ‘pluralism’ still harbors reductionist assumptions. (shrink)

This collection of new essays treats the historical, philosophical, and literary dimensions of Simone de Beauvoir's thought, and celebrates the 50th anniversary of her most influential book, The Second Sex. A team of distinguished philosophers and literary critics locate her work in the intellectual and political upheavals that marked Paris in the 1930s and 1940s; analyse her philosophical links to 17th-century rationalism, and to Kant, Hegel, Merleau-Ponty, Sartre, Simone Weil, and Heidegger; and study the connections between her philosophical and literary (...) writings. Above all, the collection tackles the relationship between theory and concrete situation with fresh insight and renewed urgency. (shrink)

The question of how and why mathematics can be applied to physical reality should be approached through the history of science, as a series of case studies which may reveal both generalizable patterns and salient differences in the grounds and nature of that application from era to era. The present examination of Descartes' Principles of Philosophy Part II, reveals a deep ambiguity in the relation of Euclidean geometry to res extensa, and a tension between geometrical form and 'common motion of (...) parts' as principles of individuation for matter in Cartesian physics. (shrink)

An adequate account of how inferences and discoveries are made in modern biology is a difficult prospect for a philosopher. Do we really deduce conclusions from Darwin’s principles? Once Darwinian biology is integrated with molecular biology, can we deduce the organism from its DNA? What does induction look like in an era where data sets are often too large to be processed by a human being? What is the role of abductive explanatory claims that try to define the biological individual (...) in relation to the microbiome with which it may be associated, or to revise the notion of evolution when the interaction of organism and environment comes to seem much more complex than earlier generations imagined. How should we evaluate “origins of life” experiments conducted in the laboratory, where chemistry shifts to biology and we try to recreate early conditions on earth to which we have no empirical access? How are the carefully controlled conditions in the lab to be brought into productive relationship with the messy, contingent outdoor work of biologists in the field, studying crabs or eelgrass at the edge of the Pacific Ocean, or prairie plants at the end of woods, on the plains of the Midwest. To answer these questions, I sent my graduate student Tano Posteraro to work with Ted Grosholz, a marine biologist at the University of California / Davis, and my undergraduate student Alex Grigas to work with Ruth Geyer Shaw, a population geneticist at the University of Minnesota. They came back with complex and interesting answers to these questions. (shrink)

The significance of Leibniz’s work as a physical scientist has long been underestimated or misunderstood. This stems in part from the great success of Newton’s physics on the one hand and the influence of Kant’s account of scientific knowledge on the other, both of which tend to obscure Leibniz’s successes and intentions. It is also due to the unavailability or scholarly neglect of key texts which, if properly assessed, illuminate the work of Leibniz in dynamics. In La dynamique de Leibniz, (...) François Duchesneau attempts to give a synoptic view of Leibniz’s accomplishments in this field, to do justice to neglected writings, and to show that the course of Leibniz’s dynamics offers fresh inspiration for current debates in the philosophy of science and epistemology. (shrink)

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential (...) to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the formulation of group theory; and geometry, transformed by Riemann, lay at the heart of topology, which in turn transformed much of modern mathematics. Using complex numbers as my case study, I argue that the best way to teach students mathematics is through a repertoire of modes of representation, which is also the best way to make mathematical discoveries. (shrink)

The significance of Leibniz’s work as a physical scientist has long been underestimated or misunderstood. This stems in part from the great success of Newton’s physics on the one hand and the influence of Kant’s account of scientific knowledge on the other, both of which tend to obscure Leibniz’s successes and intentions. It is also due to the unavailability or scholarly neglect of key texts which, if properly assessed, illuminate the work of Leibniz in dynamics. In La dynamique de Leibniz, (...) François Duchesneau attempts to give a synoptic view of Leibniz’s accomplishments in this field, to do justice to neglected writings, and to show that the course of Leibniz’s dynamics offers fresh inspiration for current debates in the philosophy of science and epistemology. (shrink)