Naturalism in Mathematics

Naturalism in Mathematics

Naturalism in Mathematics

Naturalism in Mathematics

Synopsis

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 favour of another approach--naturalism--which attends more closely to practical considerations drawn from within mathematics itself. Penelope Maddy defines naturalism, explains the motivation for it, and shows how it can be successfully applied in set theory. Her clear, original discussion is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.

Excerpt

As the title suggests, this book is in some ways a sequel to Realism in Mathematics (1990a). Though the presentation is self-contained, the central problem is a version of the issue raised in chapter 4 of the earlier work as the most pressing open problem for the set theoretic realist: how are set theoretic axioms to be judged? I now think that set theoretic realism founders (in part) on this problem, and that set theoretic naturalism provides a more promising approach. Spelling this out is the burden of what follows.

My profound and continuing debt to the writings of Quine and Gödel will be obvious from a glance at the Table of Contents; John Burgess, Tony Martin, and John Steel have also made irreplaceable contributions along the way. Jeff Barrett, Sarah Resnikoff, Jamie Tappenden, and Mark Wilson helped with conversations and correspondence, and George Boolos, Bill Harper, and Ruth Marcus with timely encouragement. Mark Balaguer, Jeff Barrett, Gary Bell, Lara Denis, Don Fallis, Tony Martin, Michael Resnik, and Jamie Tappenden read all or part of the manuscript at various stages and made valuable suggestions. My heartfelt thanks go to all these people, and to Peter Momtchiloff and Angela Blackburn for their support and guidance.

Most of this book is based on a series of articles ((1988), (1992), (1993a), (1993b), (1994), (1995), (1996b), (199?a), (199?b), (199?c), (199?d), and (199?e)); there is hardly a section that doesn't trace an ancestor in at least one of these papers. II. 4. ii and II. 6. ii contain substantial verbatim borrowings from (1993a), § 2, and (1994), 385-95, respectively. III. 6. I and ii present an expanded version of (199?d), §§ 3 and 4. Smaller extracts (from a phrase to a paragraph) appear elsewhere: I've been able to keep track of bits of (1988), § 1, in I. 3; of (199?a) in II. 6. ii; of (1996b), § 2, in III. 2; of (199?c), §§ II and III, in III. 4. iii and III. 4. iv, respectively; and of (199?d) in III. 5. My thanks to the original publishers—especially the Association for Symbolic Logic, North Holland

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.