GORDON BELOT. Geometric Possibility. Oxford and New York: Oxford University Press, 2011. ISBN 978-0-19-959532-7. Pp. x + 219

Abstract

How are we to understand the truth conditions for claims about space-time geometry, e.g., that a cyclist's front tire is trailing the rear tire of another cyclist by 10 cm, or that both cyclists are accelerating as they go downhill? A substantivalist regards the truth or falsity of such claims as underwritten by geometrical relations among the regions of space-time occupied by the tires at different times. Yet do we need to treat these claims as parasitic on structural properties of space-time? A relationalist argues that we only need the geometrical relations among bodies, but then owes us an account of the truth conditions for geometrical claims to replace the substantivalist's. Belot's aim, partially inspired by Leibniz, is to ‘retool the substantivalist truth conditions so that they demand not that certain patterns of geometric relations be (un)instantiated by actual material points, but rather that the instantiation of such patterns be geometrically (im)possible’ (p. 4). The bulk of the book is devoted to a clever and engaging exploration of different ways to flesh out this idea of ‘geometric possibility’, taken as a distinctive kind of modality.