 And the options in question would correspond to endorsing (P.7φ) or (P.8φ) for specific values of ‘φ’. At present, no thorough formal investigation has been pursued in this spirit (though see Masolo and Vieu 1999 and Hudson 2007b). Yet the issue is particularly pressing when it comes to the mereology of the spatio-temporal world. For example, it is a plausible thought that while the question of atomism may be left open with regard to the mereological structure of material objects (pending empirical findings from physics), one might be able to settle it (independently) with regard to the structure of space-time itself. This would amount to endorsing a version of either (P.7φ) or (P.8φ) in which ‘φ’ is understood as a condition that is satisfied exclusively by regions of space-time. Some may find it hard to conceive of a world in which an atomistic space-time is inhabited by entities that can be decomposed indefinitely (pace McDaniel 2006), in which case accepting (P.7φ) for regions would entail the stronger principle (P.7). However, (P.8φ) would be genuinely independent of (P.8) unless it is assumed that every mereologically atomic entity should be spatially unextended, an assumption that is not part of definition (32) and that has been challenged by van Inwagen (1981) and Lewis (1991: 32) (and extensively discussed in recent literature; see e.g. MacBride 1998, Markosian 1998a, Scala 2002, J. Parsons 2004, Simons 2004, Tognazzini 2006, Braddon-Mitchell and Miller 2006, Hudson 2006a, McDaniel 2007, Sider 2007, Spencer 2010). More generally, such issues depend on the broader question of whether the mereological structure of a thing should always “mirror” or be in perfect “harmony” with that of its spatial or spatio-temporal receptacle, a question addressed in J. Parsons (2007) and Varzi (2007: §3.3) and further discussed in Schaffer (2009), Uzquiano (2011) and Saucedo (2011). (For more on this, see the entry  location and mereology.)