 On Lewis’s view, what’s distinctive about self-locating beliefs is their content. Instead of taking the objects of belief to be possible worlds propositions, we take them to be properties. Equivalently, we can take them to be sets of centered worlds. A centered world is a set-theoretic object that models a position or a location within a world; it’s easiest to think of a centered world as a \(\langle \textrm{world}, \textrm{time}, \textrm{individual}\rangle\) triple. (Absent clever science-fictional examples, specifying a world and then a time and an individual within that world suffices to specify the intended sort of position or location. See Liao (2012) for troublemaking clever science-fictional examples, and for discussion.) Treating objects of belief as sets of centered worlds is equivalent to treating them as properties because for each property \(F\), there’s a set of centered worlds that includes a given \(\langle w,t,i\rangle\) triple iff \(i\) has \(F\) at \(t\) in \(w\), and for each set of centered worlds, there’s a property that’s shared by all and only those individuals in those worlds at those times. (Note that this requires a plenitudinous ontology of properties, to which Lewis is already independently committed. Those who subscribe to enough Lewisian metaphysics can also, equivalently, treat the objects of belief as sets of worldbound time-slices.) We will call a set of centered worlds a centered-worlds proposition or a centered proposition, and a belief with a centered-worlds proposition as its content a centered belief.