Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. She answers the traditional questions and poses a challenging new one, refocusing philosophical attention on the pressing foundational issues of contemporary mathematics.
Industry Reviews
`She has ... clearly marked out an original and interesting position.' Times Higher Education Supplement
`the book is written in a lively, engaging style. We hope that it serves to stimulate others to think seriously about issues in philosophy of mathematics because, as Maddy claims, these issues bear directly on mainstream philosophy.' Philosophy of Science
`Maddy has taken some significant steps in the right direction. It is high time more philosophers stood up for some of the important truths in Platonism. Quine took us some of the way; Maddy takes us further ... Her book is lively and accessible, of interest to both the mathematical and the philosophical amateur ... Maddy's book would be very useful in teaching courses in the philosophy of mathematics. I hope it shakes more people out of complacent
Quineanism, and into the unfinished business of naturalising mathematical knowledge.'
History and Philosophy of Logic
'In my opinion her project deserves the strongest support ... the argument she offers cannot easily be dismissed ... defenders of mathematical realism should warmly welcome Maddy's book for it offers a new store of arguments that will be very useful. Besides its scientific value and Professor Maddy's enchanting sexist language, the book is a pleasure to read. Both mathematicians with interest in philosophy and philosophers of mathematics and science will
enjoy and profit from it.'
Maria J. Frápolli, University of Granda, International Journal of the History of Mathematical Logic, Set Theory, and Foundations of Mathematics, Volume 2, no. 4, (July 1992)
'Maddy's discussion of the history of set theory is interesting, lucid, and accessible to those with limited mathematical background. Her proposed second-tier research program is also of considerable interest.'
Joan Weiner, University of Wisconsin, Philosophical Review, April 1992
'there has been consensus, among a large part of the community of analytic philosophers, that there is something deeply mysterious about our knowledge of mathematics. Maddy has provided us with an exceptionally clear statement of the worry as well as careful and sympathetic descriptions of how various philosophers have attempted to respond to it. This discussion will be invaluable both to those who want to understand the issue and to those who want to
address it.'
The Philosophical Review
'Maddy has written a concise and lucid book which covers not only her own ideas on set-theoretic realism and the "reality" of mathematics, but also provides a useful summary of the old and continuing debates surrounding mathematical ontology. This feature makes the book ideal as a classroom text ... this book makes a valuable contribution to the literature simply by providing the language of set-theoretic realism with which to discuss this problem.'
Lilianne Rivka Kfia, Review of Metaphysics, March 1994
'a delightful, thought-provoking book which contains interesting ideas on almost every page ... It is a great virtue of Realism in Mathematics that it presents so many recent ideas and arguments in the philosophy of mathematics so clearly. This will make the book very useful to a wide range of readers. Maddy is also very good about summarizing her own arguments at various stages as her discussion unfolds. The book contains many excellent
expositions of positions in the philosophy of mathematics and a nice survey of recent work in set theory. Polemics aside, it also constitutes a remarkable effort to forge a new position in the philosophy of mathematics and
it can be highly recommended.'
Richard Tieszen, The Philosophical Journal of The Canadian Society for History and Philosophy of Mathematics, Series III, 1994
`She sets herself the task of presenting her views in a manner 'accessible to both non-philospohical mathematicians and non-mathematical philosophers [as well as] students and interested amateurs'. This is a worthy aim, and the extent to which she achieves it is admirable. She is particularly adept at sketching in the background to the philosophical and mathematical problems that arise along the way.'
Colin Cheyne, University of Otago, Meta Science, New Series Issue Six 1994
