 Thick propositions are hyperintensional. They cut at least as finely as ordinary sets of worlds: when \(|A|\) differs from \(|B|\), [\(A\)] will differ from [\(B\)]. Additionally, there will be \(A\)’s and \(B\)’s expressing different thick propositions in spite of being true at the same worlds, because they are about different things: \(s(A)\) will differ from \(s(B)\) even if \(|A| = |B|\). For example, “There is an even number of stars or there is not” and “There are no non-self-identical Italian restaurants” are both necessarily true, but they correspond to distinct thick propositions because of their different subject matters. The suggestion that adding subject matter to semantics is the key to handling hyperintensionality is discussed in Gioulatou (2016).