New Directions In The Philosophy Of Mathematics

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

This volume sheds light on still unexplored issues and raises new questions in the main areas addressed by the philosophy of science. Bringing together selected papers from three main events, the book presents the most advanced scientific results in the field and suggests innovative lines for further investigation. It explores how discussions on several notions of the philosophy of science can help different scientific disciplines in learning from each other. Finally, it focuses on the relationship between Cambridge and Vienna in twentieth century philosophy of science. The areas examined in the book are: formal methods, the philosophy of the natural and life sciences, the cultural and social sciences, the physical sciences and the history of the philosophy of science.

This examination of a series of philosophical issues arising from the applicability of mathematics to science consists of scientifically-informed philosophical analysis and argument. One distinctive feature of this project is that it proposes to look at issues in philosophy of mathematics within the larger context of philosophy of science.

In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.

The Quantum of Explanation advances a bold new theory of how explanation ought to be understood in philosophical and cosmological inquiries. Using a complete interpretation of Alfred North Whitehead’s philosophical and mathematical writings and an interpretive structure that is essentially new, Auxier and Herstein argue that Whitehead has never been properly understood, nor has the depth and breadth of his contribution to the human search for knowledge been assimilated by his successors. This important book effectively applies Whitehead’s philosophy to problems in the interpretation of science, empirical knowledge, and nature. It develops a new account of philosophical naturalism that will contribute to the current naturalism debate in both Analytic and Continental philosophy. Auxier and Herstein also draw attention to some of the most important differences between the process theology tradition and Whitehead’s thought, arguing in favor of a Whiteheadian naturalism that is more or less independent of theological concerns. This book offers a clear and comprehensive introduction to Whitehead’s philosophy and is an essential resource for students and scholars interested in American philosophy, the philosophy of mathematics and physics, and issues associated with naturalism, explanation and radical empiricism.

Dale Jacquette charts the development of Schopenhauer's ideas from the time of his early dissertation on The Fourfold Root of the Principle of Sufficient Reason through the two editions of his magnum opus The World as Will and Representation to his later collections of philosophical aphorisms and competition essays. Jacquette explores the central topics in Schopenhauer's philosophy including his metaphysics of the world as representation and Will, his so-called pessimistic philosophical appraisal of the human condition, his examination of the concept of death, his dualistic analysis of free will, and his simplified non-Kantian theory of morality. Jacquette shows how these many complex themes fit together in a unified portrait of Schopenhauer's philosophy. The synthesis of Plato, Kant and Buddhist and Hindu ideas is given particular attention as is his influence on Nietzsche, first a follower and then arch opponent of Schopenhauer's thought, and the early Wittgenstein. The book provides a comprehensive and in-depth historical and philosophical introduction to Schopenhauer's distinctive contribution to philosophy.

With the failure of economics to predict the recent economic crisis, the image of economics as a rigorous mathematical science has been subjected to increasing interrogation. One explanation for this failure is that the subject took a wrong turn in its historical trajectory, becoming too mathematical. Using the philosophy of mathematics, this unique book re-examines this trajectory. Philosophy of Mathematics and Economics re-analyses the divergent rationales for mathematical economics by some of its principal architects. Yet, it is not limited to simply enhancing our understanding of how economics became an applied mathematical science. The authors also critically evaluate developments in the philosophy of mathematics to expose the inadequacy of aspects of mainstream mathematical economics, as well as exploiting the same philosophy to suggest alternative ways of rigorously formulating economic theory for our digital age. This book represents an innovative attempt to more fully understand the complexity of the interaction between developments in the philosophy of mathematics and the process of formalisation in economics. Assuming no expert knowledge in the philosophy of mathematics, this work is relevant to historians of economic thought and professional philosophers of economics. In addition, it will be of great interest to those who wish to deepen their appreciation of the economic contours of contemporary society. It is also hoped that mathematical economists will find this work informative and engaging.