 One may hope for a total ordering of hyperintensional notions by fine-grainedness, i.e., an ordering such that any two given ones are comparable: given any \(X\) and \(Y\), either \(X\) is at least as fine-grained as \(Y\), or vice versa. But one can show that the simple setting is wrong. One can provide intuitive examples (inspired by Hornischer 2017, which also includes a thorough discussion) of incomparable hyperintensional operators: \(X\) and \(Y\) for which there are sentences \(A\), \(B\), \(C\), \(D\), such that \(XA\) and \(XB\) are equivalent but \(YA\) and \(YB\) are not, \(YC\) and \(YD\) are equivalent but \(XC\) and \(XD\) are not.