New Directions in the Philosophy of Mathematics: An Anthology

"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." "After almost a century in which the attempt was made to reduce philosophy of mathematics to set theory, philosophers have begun to reconsider the traditional approaches. The Tymoczko volume provides a solid intro to these new approaches, that is both readable and insightful. A background in formal logic, or traditional philosophy of mathematics, is not presupposed, as there are basic essays that should get the reader up to speed on the terminology. Nor does one have to be a mathematician to appreciate the thoughts presented. At the same time, I don't believe any mathematician would be offended or alarmed by the presentations of this book. Ultimately, there is no final consensus offered. Rather, the topic is reinvigorated with a collection of fresh approaches that do not falsify the experience of mathematics by trying to reduce it to something else."