For any objects x and y in any possible world, if x has exact location r1 and y has exact location r2, and r1 and r2 overlap, then given Supersubstantivalism+, x is identical to r1 and y is identical to r2
When two spaces or regions share some of the same area or coordinates.
possible world(Leibniz's account of modality; 'existence' of possible worlds is shorthand for compossibility, not literal existence)
A set of compossible essences — a maximal collection of individual natures that can co-exist without contradiction
supersubstantivalism(Used to argue for the restricted version of No Interpenetration)
The view under which material objects are identified with or essentially tied to spatial regions, such that disjoint material objects cannot share exact locations
Supersubstantivalism+ entails No Interpenetration. Take any objects x and y in any possible world, and suppose that they have exact locations, r1 and r2 respectively, that overlap. Then, given Supersubstantivalism+, x=r1 and y=r2, hence x and y overlap.