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A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholarsMathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics.Written by oystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Godel, W. V. Quine, Paul Benacerraf, and Hartry H. Field.Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

Philosophical Logic is a clear and concise critical survey of nonclassical logics of philosophical interest written by one of the world's leading authorities on the subject. After giving an overview of classical logic, John Burgess introduces five central branches of nonclassical logic (temporal, modal, conditional, relevantistic, and intuitionistic), focusing on the sometimes problematic relationship between formal apparatus and intuitive motivation. Requiring minimal background and arranged to make the more technical material optional, the book offers a choice between an overview and in-depth study, and it balances the philosophical and technical aspects of the subject. The book emphasizes the relationship between models and the traditional goal of logic, the evaluation of arguments, and critically examines apparatus and assumptions that often are taken for granted. Philosophical Logic provides an unusually thorough treatment of conditional logic, unifying probabilistic and model-theoretic approaches. It underscores the variety of approaches that have been taken to relevantistic and related logics, and it stresses the problem of connecting formal systems to the motivating ideas behind intuitionistic mathematics. Each chapter ends with a brief guide to further reading. Philosophical Logic addresses students new to logic, philosophers working in other areas, and specialists in logic, providing both a sophisticated introduction and a new synthesis.

One of the world's leading epistemologists provides a sophisticated, revisionist introduction to the subjectIn this concise book, one of the world's leading epistemologists provides a sophisticated, revisionist introduction to the problem of knowledge in Western philosophy. Modern and contemporary accounts of epistemology tend to focus on limited questions of knowledge and skepticism, such as how we can know the external world, other minds, the past through memory, the future through induction, or the world's depth and structure through inference. This book steps back for a better view of the more general issues posed by the ancient Greek Pyrrhonists. Returning to and illuminating this older, broader epistemological tradition, Ernest Sosa develops an original account of the subject, giving it substance not with Cartesian theology but with science and common sense.Descartes is a part of this ancient tradition, but he goes beyond it by considering not just whether knowledge is possible at all but also how we can properly attain it. In Cartesian epistemology, Sosa finds a virtue-theoretic account, one that he extends beyond the Cartesian context. Once epistemology is viewed in this light, many of its problems can be solved or fall away.The result is an important reevaluation of epistemology that will be essential reading for students and teachers.

An essential introduction to the philosophy of biologyThis is a concise, comprehensive, and accessible introduction to the philosophy of biology written by a leading authority on the subject. Geared to philosophers, biologists, and students of both, the book provides sophisticated and innovative coverage of the central topics and many of the latest developments in the field. Emphasizing connections between biological theories and other areas of philosophy, and carefully explaining both philosophical and biological terms, Peter Godfrey-Smith discusses the relation between philosophy and science; examines the role of laws, mechanistic explanation, and idealized models in biological theories; describes evolution by natural selection; and assesses attempts to extend Darwin's mechanism to explain changes in ideas, culture, and other phenomena. Further topics include functions and teleology, individuality and organisms, species, the tree of life, and human nature. The book closes with detailed, cutting-edge treatments of the evolution of cooperation, of information in biology, and of the role of communication in living systems at all scales.Authoritative and up-to-date, this is an essential guide for anyone interested in the important philosophical issues raised by the biological sciences.