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Philosophy of Mathematics
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. 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 Gödel 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.
The Upswing
From the author of Bowling Alone and Our Kids, a “sweeping yet remarkably accessible” (The Wall Street Journal) analysis that “offers superb, often counterintuitive insights” (The New York Times) to demonstrate how we have gone from an individualistic “I” society to a more communitarian “We” society and then back again, and how we can learn from that experience to become a stronger, more unified nation. Deep and accelerating inequality; unprecedented political polarization; vitriolic public discourse; a fraying social fabric; public and private narcissism—Americans today seem to agree on only one thing: This is the worst of times. But we’ve been here before. During the Gi...
The Spirit of Missions
Includes the proceedings of the annual meeting of the Society.
Putnam and Beyond
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chos...
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Following Putnam’s Trail
Following Putnam’s Trail addresses Putnam’s path through important philosophical problems. One outstanding feature of Putnam’s philosophy has been his contribution to the development of American pragmatism as well as his many changes of mind when thinking about realism. Realism and pragmatism are indeed the central focus of the contributions to the volume. The book includes a defence of pragmatism by Putnam himself, and several commentaries on it. This volume should be of interest both to scholars who specialize in analytical philosophy as well as to those who have a wider interest in philosophy.
Our Kids
"The bestselling author of Bowling Alone offers [an] ... examination of the American Dream in crisis--how and why opportunities for upward mobility are diminishing, jeopardizing the prospects of an ever larger segment of Americans"--
