 One significant worry about the right-to-left direction of  Indiscernibility  arises for those who posit higher-order perfectly natural properties, whose instances are properties or propositions rather than objects. For example, someone who posited that thinking was a perfectly natural relation between people and propositions, modally independent of the perfectly natural properties instantiated only by objects, one would likely want to rule out the possibility that there are qualitatively indiscernible people \(x\) and \(y\) such that \(x\) thinks that \(x\) is hungry, \(y\) does not think that \(y\) is hungry.  Indiscernibility  does not obviously do this. 