Penelope Maddy Naturalism in Mathematics

ISBN 13: 9780198250753

Naturalism in Mathematics

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9780198250753: Naturalism in Mathematics
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Naturalism in Mathematics investigates how the most fundamental assumptions of mathematics can be justified. One prevalent philosophical approach to the problem--realism--is examined and rejected in favor of another approach--naturalism. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

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About the Author:


Penelope Maddy is Professor of Philosophy at the University of California, Irvine, having previously held positions at the University of Illinois, Chicago, and the University of Notre Dame.

Review:


"Stylistically the book is an enjoyably readable and beautifully clear. In particular Maddy has a near-miraculous gift for explaining mathematical technicalities in a way that is comprehensible to the non-expert. The book is therefore well worth reading not just for the new and bold philosophical position it promotes, but also as a philosopher's guide to what is going on in contemporary set theory." The Philosophical Review


"Maddy's knowledge of early and contemporary set theory, and of philosophically significant parts of the history of mathematics generally, is impressively wide and deep, and her discussions of these matters are illuminating and rewarding. She writes in a clear, forthright and challenging style. Her book is eminently readable, instructive, and thought-provoking."--The Journal of Symbolic Logic


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Book Description Oxford University Press, United Kingdom, 2000. Paperback. Condition: New. Revised ed.. Language: English . Brand New Book ***** Print on Demand *****. Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view-realism-is assessed and finally rejected in favour of another- naturalism-which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy s clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines. Seller Inventory # AAV9780198250753

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Book Description Oxford University Press, United Kingdom, 2000. Paperback. Condition: New. Revised ed.. Language: English . Brand New Book ***** Print on Demand *****.Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view-realism-is assessed and finally rejected in favour of another- naturalism-which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy s clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines. Seller Inventory # AAV9780198250753

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