It is sometimes suggested that impure sets are spatially co-located with their members (and hence are located in space). Sets, however, are in important respects like numbers. In particular, sets are connected to concepts in much the same manner as numbers are connected to concepts—in both cases, they are fundamentally abstracts of (or corresponding to) concepts. This parallel between the structure of sets and the structure of numbers suggests that the metaphysics of sets and the metaphysics of numbers should parallel (...) each other in relevant ways. This entails, in turn, that impure sets are not co-located with their members (nor are they located in space). (shrink)

Hud Hudson offers a fascinating examination of philosophical reasons to believe in hyperspace. He explores non-theistic reasons in the first chapter and theistic ones towards the end; in the intervening sections he inquires into a variety of puzzles in the metaphysics of material objects that are either generated by the hypothesis of hyperspace or else informed by it, with discussions of receptacles, boundaries, contact, occupation, and superluminal motion. Anyone engaged with contemporary metaphysics, and many philosophers of religion, will find much (...) to stimulate them here. (shrink)

I have previously argued in a paper with Robson that a particular time travel scenario favours perdurantism over endurantism on the grounds that endurantists must give up on the Weak Supplementation Principle. Smith has responded, arguing that the reasons we provided are insufficient to warrant this conclusion. This paper agrees with that conclusion (for slightly different reasons: that even the perdurantist has to give up on the Weak Supplementation Principle) but argues that the old argument can be supplanted with a (...) new one. (shrink)