 On closed set logic and boundaries as a natural setting for contradictory theories, see Mortensen (2003, 2010). Weber and Cotnoir (2015) also explore the inconsistency of boundaries, arising from the incompatibility of the three principles (i) there are boundaries, (ii) space is topologically connected, and (iii) discrete entities can be in contact (i.e., no space between them). This is a very interesting problem, as all three are plausible; in particular there do seem to be boundaries in our world. An initially surprising feature of this account is that boundaries come out as “empty”; after all, null entities are contrary to the spirit of mereology. But this is not so shocking as it turns out that they are only empty in the sense that they have members inconsistently.