The Matter of Points
This chapter turns to metaphysical matters. Some analytic metaphysicians have occupied themselves with the nature (or the possible nature) of space and time (or space–time), and with the relationship between physical objects and the regions of space or space–time they occupy. Some of the issues concern the boundaries of objects and the notion of contact. The first goal is to give a somewhat biased overview of a portion of this literature, arguing that many of the issues are much easier to negotiate if we assume a regions-based space or space–time. The chapter then turns to some apparent limitations of the semi-Aristotelian accounts of space or space–time. For example, the natural analogue of Lebesgue measure is not countably additive (although it is finitely additive), and there seems to be no straightforward way to account for continuous variation in our frameworks other than by just introducing “points” via “extensive abstraction”. Finally, the question is broached of adjudicating whether space or space–time really is punctiform. The tight connection between our regions-based, gunky theories and the more standard Dedekind–Cantor punctiform theories indicates that space or space–time can be described, completely and adequately either way.