James Franklin. An Aristotelian Realist Philosophy of Mathematics. New York: Palgrave Macmillan, 2014. ISBN: 978-1-137-40072-7 (hbk); 978-1-137-40073-4 (pdf); 978-1-137-40074-1 (e-book). Pp. x + 308

Most of the traditional problems in the philosophy of mathematics arise, in James Franklin's words, out of the ‘oscillation between Platonism and nominalism, as if those were the only alternatives’ (p. 11). In An Aristotelian Realist Philosophy of Mathematics Franklin develops a tantalizing alternative to these approaches by arguing that at least some mathematical universals exist in the physical realm and are knowable through ordinary methods of access to physical reality. By offering a third option that lies between these extreme all-or-nothing approaches and by rejecting the ‘dichotomy of objects into abstract and concrete’, Franklin provides potential solutions to many of these traditional problems and opens up a whole new terrain for debate in the philosophy of mathematics (p. 15). The acknowledgement of this by no means new but oft neglected Aristotelian position...