TEXTBOOK REVIEW TO INFINITY AND BEYOND! Miche` le Friend, Introducing Philosophy of Mathematics. Stocksfield: Acumen Publishing, 2007. Pp. ix. + 176. £16.99 PB. £50.00 HB. By Fabien Medvecky This book is aimed at senior undergraduates. So it might be assumed that it would be a straightforward run through the vari- ous positions in the philosophy of mathematics. But Friend does more than that; she invites the reader to engage with the different positions in the philosophy of mathematics by considering these positions in relation to infinity and the issues that the concept raises. The prospect is appealing, as infinity can help to highlight both the difficulties with, and the differences between, philosophies of mathematics. It is within this framework that Friend presents the major, as well as some less-discussed, philosophical views. The first two chapters are used to set up a basis from which to assess these views. Friend first discusses infinity, and then pre- sents the Platonist/realist view. The discussion on infinity opens with a presentation of three of Zeno’s paradoxes. This is followed by some discussion of the difference between potential and actual infinity, and between ordinal and cardinal infinity. Friend discusses, in great depth, the notion of cardinal infinity, and this leads into a presentation of some of the issues arising out of infinite sets. She discusses the Ôcontinuum problem’ which asks whether there exists a set whose cardinality is between that of the natural numbers and that of the real numbers. Related to the continuum problem is the use of power sets, which introduce multiple (in fact infinitely many) infinities. As might be expected, the concepts presented in relation to infinity are reasonably technical, yet Friend is careful and thor- ough enough to ensure the concepts discussed are both clear and well understood. Metascience (2008) 17:225–229 Ó Springer 2008 DOI 10.1007/s11016-008-9180-7