Philosophy of Mathematics: Structure and Ontology - Tapa dura

real realists will feel, Shapiro's book is an important contribution to the philosophy of mathematics. It fills a major gap: although structuralism has seemed to many a promising idea, we have not previously had so sustained and thorough a treatment of its metaphysical and ontological implications. Everyone interested in the subject will have much to learn from this rich and intriguing book. (Keith Hossack, The Philosophical Quarterly, Vol 50, No 198 January 2000)

Shapiro is admirably candid about the limits of structuralism in dealing with mathematical applicability ... There is a lot more in this fair, judicious, and informative book than I have been able to indicate in the scope of a short review. Whether or not the reader is persuaded by Shapiro's structuralism, one can learn a great deal about contemporary philosophy of mathematics from the book. (Mark Steiner, The Hebrew University of Jerusalem, Jerusalem Philosophy Quarterly, vol 48, July 1999)

Insightful. The Economist (UK), February 2000

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout its history and covers historical figures, such as Plato, Aristotle, Kant, and Mill. It presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.