Leon Horsten.* The Metaphysics and Mathematics of Arbitrary Objects. Cambridge University Press, 2019. Pp. xviii + 231. ISBN: 978-1-107- 03941-4 (hbk); 978-1-10860177-1 (e-book). doi: 10.1017/9781139600293.

摘要

Leon Horsten's The Metaphysics and Mathematics of Arbitrary Objects is an important contribution to a relatively neglected area of analytic metaphysics: arbitrary objects. Building on Fine's seminal work 1985, Horsten develops a new theory of arbitrary objects which not only aims to improve upon Fine's original theory in various ways, but also to shed new light on disparate philosophical issues. These include the coherence of the nineteenth-century conception of variable mathematical quantities, realist/anti-realist debates about structure within the philosophy of mathematics, and the conception of random variables within statistics. Indeed, Horsten shows how his conception of arbitrary objects fruitfully extends to the natural numbers, mathematical structures more generally, and, at least to a certain extent, random variables.