  Here we return to issues concerning the metaphysics of quantum field theory and it is worth pointing out that underdetermination may arise here too. In classical physics we are faced with a choice between the view of the field as a kind of global substance or stuff and an alternative conception in terms of field quantities assigned to and hence as properties of, the points of space-time. In the case of quantum field theory, the field quantities are not well-defined at such points (because of difficulties in defining exact locational states in quantum field theory) but are instead regarded as ‘smeared’ over space-time regions (see Teller 1999). The underdetermination remains, of course: between an understanding of the given quantum field in terms of some kind of global substance and the alternative conception in terms of the properties of space-time regions. Taking the first option obviously requires a metaphysically articulated form of substantivalism applicable to quantum field theory. Many commentators have preferred the second option, but now, of course, attention must be paid to the metaphysical status of the space-time regions over which the field properties are taken to be instantiated. Typically, these will be taken to be composed of points of space-time and conceiving of a field in terms of a set of properties meshes comfortably with the approach that takes space-time to be a kind of substance or ‘stuff’ itself. But this too faces well known difficulties in the context of modern physics (see, for example, Earman 1989). In particular, space-time substantivalism has been argued to have extremely unpalatable consequences (Earman and Norton 1987). Unfortunately, such a properties-based account of fields is difficult to reconcile with the alternative view of space-time as merely a system of relations (such as contiguity) between physical bodies: if the field quantities are properties of space-time regions and the latter are understood, ultimately, to be reducible to relations between physical objects, where the latter are conceived of in field-theoretic terms, then a circularity arises (see Rovelli 1999). One way forward would be to draw on alternative accounts of the nature of spacetime. Thus Stachel has suggested that we drop the sharp, metaphysical distinction between things and relations between things and adopt a broadly ‘structuralist’ view of spacetime (Stachel 1999; see the essays in Rickles, French &amp; Saatsi 2006). Suitably extended, such a ‘structuralist’ approach might offer a way around the above incompatibility by regarding both space-time and the quantum field in structural terms, rather than in terms of substances, properties or relations (see Auyang 1995; Cao 2003; French and Ladyman 2003; Kantorovich 2003; Lyre 2004; Saunders 2003b).