Book Review : The Metaphysics and Mathematics of Arbitrary Objects

Consider the arbitrary triangle. It is a closed planar figure with three sides and three angles that add up to 180 degrees (in a Euclidean geometry). On the one hand, saying this does not necessarily commit me to the existence of such an object as the arbitrary triangle. For although ‘the arbitrary triangle’ seems at first glance to be a singular term, familiar methods allow us to deny that it actually refers to anything. On the other hand, it is coherent to accept the existence of the arbitrary triangle, since Kit Fine’s (1985) Reasoning with Arbitrary Objects provided the tools to take apparent reference to arbitrary objects literally. Although Fine’s work is well known, it has not been widely taken up. Leon Horsten believes “that Fine’s ideas in this area deserve a better fate and [he wants] to play a role in bringing this about” (3). This book represents his efforts towards that end.