Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures

Routledge, 2008. — 264 p. This book offers an intriguing sample of both traditional and current ideas in the philosophy of mathematics. Its readable style is aimed at those with more background in philosophy than in mathematics, with detailed examples usually involving only secondary-level algebra and geometry. The author (philosophy, Univ. of Toronto) states that one of his goals is to argue for Platonism. This attempt is not entirely convincing, both because some of Browns positions need more substantiation and because alternative views are presented only insofar as they can be readily dismissed. As the subtitle suggests, a unique feature is the interesting argument in favor of the validity and usefulness of pictures (not limited to geometrical diagrams) as proofs in and of themselves. It is to be hoped that a few mathematically substantive typographical errors in the examples will be corrected in the finished edition. For academic mathematics and philosophy collections.Kristine Fowler, Mathematics Lib., Univ. of Minnesota, Minneapolis