This chapter argues that we have inconsistent intuitions about the structure of space (or spacetime, or some stuff, the aether, that fills space or spacetime). A contradiction is obtained from eleven premises, each of which is either directly intuitive or supported by intuitions. The use of so many premises results from the desire to exhibit as clearly as possible the places where one might decide some intuition is to be undermined. Nonetheless the argument for inconsistency is straightforward: …
Read moreThis chapter argues that we have inconsistent intuitions about the structure of space (or spacetime, or some stuff, the aether, that fills space or spacetime). A contradiction is obtained from eleven premises, each of which is either directly intuitive or supported by intuitions. The use of so many premises results from the desire to exhibit as clearly as possible the places where one might decide some intuition is to be undermined. Nonetheless the argument for inconsistency is straightforward: our intuitions support the existence of a _supersponge_, namely a region of less than the total volume but not disjoint from any connected part of space of positive diameter. But the complement of a supersponge is an intuitively impossible region. Yet, intuitively a region of less than maximal volume must have a complement. So some intuition must be abandoned.
